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What is the length of a side of a square shaped piece of cardboard of area 1225 cm\(^2\)?
|
35 cm |
What is the length of a side of a square of area the same as that of a rectangle of length 27 cm and breadth 12 cm?
|
18 cm |
196 children participating in a drill display have been placed such that they form an equal number of rows and columns. How many children are there in a row?
|
14 |
The surface area of a cube is 1350 cm\(^2\). Find the length of a side of the cube.
|
15 cm |
A rectangular walkway has been made by placing 10 flat square shaped concrete slabs along 200 rows. If the area of the flat surface of a concrete slab is 231.04 cm\(^2\), what is the length and the breadth of the walkway?
|
Length: 3040 cm, Breadth: 152 cm |
The length and breadth of a rectangular shaped plot of land are respectively 25 m and 12 m. Find to the nearest metre, the least distance that a child standing at one corner of the plot should travel to reach the diagonally opposite corner of the plot.
|
28 m |
If the length of the hypotenuse of an isosceles right angled triangle is 12 cm, find the length of a remaining side. (Give the answer to two decimal places).
|
8.49 cm |
If \(\frac{3}{4}\) of a tank which was completely filled with water was used by a household for its needs on a certain day, what fraction of the tank still held water by the end of the day?
|
\(\frac{1}{4}\) |
If the two pieces of wire \(A\) and \(B\) are of unequal length, is \(\frac{1}{3}\) of the length of \(A\) equal to \(\frac{1}{3}\) of the length of \(B\), or are they unequal? Give reasons for your answer.
|
Unequal, because \(\frac{1}{3}\) of different lengths are different. |
Mother, who went to the market with Rs 500 in hand, spent Rs 300 to buy vegetables. What fraction of the money in hand did she spend on vegetables?
|
\(\frac{3}{5}\) |
Mother, who went to the market with Rs 500 in hand, spent Rs 150 to buy fruits. What fraction of the money in hand did she spend on fruits?
|
\(\frac{3}{10}\) |
Mother, who went to the market with Rs 500 in hand, spent Rs 300 to buy vegetables and spent Rs 150 to buy fruits. Mother had planned to save \(\frac{1}{4}\) of the money she had taken to the market. Was she able to fulfill her plan? Give reasons for your answer.
|
No, because she spent Rs 450 and saved Rs 50, which is \(\frac{1}{10}\) of the total money. |
Sathis travelled \(\frac{1}{4}\) of the journey by bicycle and \(\frac{2}{3}\) by bus. Rest of the journey traveled by three wheeler. What fraction of the total journey did he travel by both bicycle and bus?
|
\(\frac{11}{12}\) |
Sathis travelled \(\frac{1}{4}\) of the journey by bicycle and \(\frac{2}{3}\) by bus. Rest of the journey traveled by three wheeler. What fraction of the whole journey remained for Sathis to travel by three wheeler?
|
\(\frac{1}{12}\) |
Mr. Upul received Rs 24 000 as his salary last month. He spent \(\frac{3}{8}\) of it for travel expenses. Find the amount he spent for travel expenses.
|
9000 |
A household water tank was filled with water. When \(\frac{3}{4}\) of its volume was used up, there was 200 \(l\) of water remaining in the tank. What fraction of the whole tank was the remaining volume of water equal to?
|
\(\frac{1}{4}\) |
A household water tank was filled with water. When \(\frac{3}{4}\) of its volume was used up, there was 200 \(l\) of water remaining in the tank. Find the capacity of the tank.
|
800 \(l\) |
\(\frac{3}{7}\) of a plot of land belonged to Pradeep. He bought \(\frac{1}{4}\) of the portion of land which did not belong to him, and annexed it to his plot. What fraction of the total plot of land did Pradeep buy?
|
\(\frac{1}{7}\) |
\(\frac{3}{7}\) of a plot of land belonged to Pradeep. He bought \(\frac{1}{4}\) of the portion of land which did not belong to him, and annexed it to his plot. If the area of the portion remaining after Pradeep had bought a part of it is 240 m², what is the area of the land owned by Pradeep in square metres?
|
320 m² |
Mohamed wrote exactly half of his land in his daughter's name and \(\frac{1}{3}\) of his land in his son’s name. He donated the remaining 10 acres to a charity. What fraction of the total plot of land did Mohamed donate to charity?
|
\(\frac{1}{6}\) |
Mohamed wrote exactly half of his land in his daughter's name and \(\frac{1}{3}\) of his land in his son’s name. He donated the remaining 10 acres to a charity. How many acres is the whole plot of land?
|
60 acres |
Mohamed wrote exactly half of his land in his daughter's name and \(\frac{1}{3}\) of his land in his son’s name. He donated the remaining 10 acres to a charity. Since the land that was donated to charity was not sufficient, his daughter was willing to give a portion of what she received, so that the land that the charity received would be double the initial amount. Show that when this is done, the plots that the daughter and the son have are equal in area.
|
Daughter and son each have 20 acres. |
Black pepper and cloves have been cultivated in \(\frac{7}{8}\) of a plot of land. Black pepper has been cultivated in 450 m\(^2\) while cloves have been cultivated in \(\frac{1}{4}\) of the land. Find the fraction of land on which black pepper has been cultivated.
|
\(\frac{5}{8}\) |
Black pepper and cloves have been cultivated in \(\frac{7}{8}\) of a plot of land. Black pepper has been cultivated in 450 m\(^2\) while cloves have been cultivated in \(\frac{1}{4}\) of the land. Find the area of the whole land.
|
720 m\(^2\) |
Black pepper and cloves have been cultivated in \(\frac{7}{8}\) of a plot of land. Black pepper has been cultivated in 450 m\(^2\) while cloves have been cultivated in \(\frac{1}{4}\) of the land. Find the area in which cloves have been cultivated.
|
180 m\(^2\) |
A piece of wire was cut into three equal parts. One of the three parts was cut again into four equal pieces. What fraction of the length of the whole piece of wire is the length of one small piece?
|
\(\frac{1}{12}\) |
A piece of wire was cut into three equal parts. One of the three parts was cut again into four equal pieces. If a small piece of wire is 70 cm in length, find the length of the whole wire.
|
840 cm |
Mr. Austin spends \(\frac{2}{5}\) of his salary on food. What fraction of his salary remains after he has spent for his food?
|
\(\frac{3}{5}\) |
Mr. Austin spends \(\frac{2}{5}\) of his salary on food. Mr. Austin sends \(\frac{2}{3}\) of the remaining amount to his wife after spending on food. What fraction of his salary does he send his wife?
|
\(\frac{2}{5}\) |
Mr. Austin spends \(\frac{2}{5}\) of his salary on food. Mr. Austin sends \(\frac{2}{3}\) of the remaining amount to his wife after spending on food. What fraction of Mr. Austin's salary is left over after spending on food and sending money to his wife?
|
\(\frac{1}{5}\) |
From a certain amount of money, \(\frac{1}{2}\) was given to \(A\), \(\frac{1}{3}\) of the remaining amount was given to \(B\), and the rest was given to \(C\). Find the fraction that \(C\) received from the amount that was distributed.
|
\(\frac{1}{3}\) |
From a certain amount of money, \(\frac{1}{2}\) was given to \(A\), \(\frac{1}{3}\) of the remaining amount was given to \(B\), and the rest was given to \(C\).
If instead of dividing the amount in the above manner, it was divided equally between the three, show that the amount that \(B\) would receive is twice the amount that he received initially.
|
\(\frac{1}{3}\) (equal share) is twice \(\frac{1}{6}\) (initial share). |
From a certain amount of money, \(\frac{1}{2}\) was given to \(A\), \(\frac{1}{3}\) of the remaining amount was given to \(B\), and the rest was given to \(C\).
If \(C\) received Rs 1000 through the distribution, find the total amount that was distributed among the three.
|
Rs 3000 |
It has been decided to allocate \(\frac{2}{3}\) of the floor area of a certain hall for classrooms, \(\frac{2}{3}\) of the remaining portion for an office, and the rest of the floor area, which is 200 m² for the library. What fraction of the whole area has been allocated for the office?
|
\(\frac{2}{9}\) |
It has been decided to allocate \(\frac{2}{3}\) of the floor area of a certain hall for classrooms, \(\frac{2}{3}\) of the remaining portion for an office, and the rest of the floor area, which is 200 m² for the library. What fraction of the whole area has been allocated for the library?
|
\(\frac{1}{9}\) |
It has been decided to allocate \(\frac{2}{3}\) of the floor area of a certain hall for classrooms, \(\frac{2}{3}\) of the remaining portion for an office, and the rest of the floor area, which is 200 m² for the library. Find the floor area of the hall.
|
1800 m² |
It has been decided to allocate \(\frac{2}{3}\) of the floor area of a certain hall for classrooms, \(\frac{2}{3}\) of the remaining portion for an office, and the rest of the floor area, which is 200 m² for the library. Find separately the floor area that is allocated for the classrooms and the office.
|
Classrooms: 1200 m², Office: 400 m² |
Of the amount that Anil spent on a trip, \(\frac{4}{7}\) was spent on food and \(\frac{2}{3}\) of the remaining amount on travelling. If Rs 800 was spent on other expenses, find how much Anil spent in total on the trip.
|
Rs 5600 |
Saroja read \(\frac{1}{3}\) of a book she borrowed from the library on the first day. On the second day she was only able to read \(\frac{1}{2}\) of the remaining portion. On the third day, she finished the book by reading the remaining 75 pages. How many pages were there in total in the book?
|
225 pages |
\( A, B \) and \( C \) are the three owners of a business. The profit from the business was divided between the three of them based on the amount they each invested. \( A \) received \(\frac{2}{7}\) of the profit, \( B \) received twice the amount \( A \) received, and \( C \) received the remaining portion. If the total amount that \( A \) and \( B \) received together is Rs 72 000, find the profit from the business.
|
Rs 84 000 |
An election was held between two persons to select a representative to a certain institution. All the voters who were registered cast their votes. The winner received \(\frac{7}{12}\) of the votes and won by a majority of 120 votes. What fraction of the total votes did the person who lost receive?
|
\(\frac{5}{12}\) |
An election was held between two persons to select a representative to a certain institution. All the voters who were registered cast their votes. The winner received \(\frac{7}{12}\) of the votes and won by a majority of 120 votes. How many registered voters were there?
|
720 |
An election was held between two persons to select a representative to a certain institution. All the voters who were registered cast their votes. The winner received \(\frac{7}{12}\) of the votes and won by a majority of 120 votes. Find the number of votes the winner received.
|
420 |
If the length of a rectangular shaped field is \( (2a + 7) \) m and the breadth is \( (2a - 3) \) m, determine the area of the field in terms of \( a \).
|
\(4a^2 + 8a - 21\) m\(^2\) |
Piyumi made a square-shaped flower bed. Her sister made a rectangular flower bed. The length of the sister's bed was 3 metres more than that of Piyumi's and the width was 2 metres less than that of Piyumi's. Taking the length of one side of Piyumi's bed as \( x \), write the length and width of the sister's bed in terms of \( x \) and then express its area in the form \( Ax^2 + Bx + C \).
|
Length: \(x + 3\), Width: \(x - 2\), Area: \(x^2 + x - 6\) |
A child bought \(a\) mandarins which were priced at \(x\) rupees each. He then decides to buy three times that number of apples. The price of an apple is twice the price of a mandarin. Write an expression in terms of \(a\) and \(x\) for the cost of the apples.
|
\(6ax\) |
A child bought \(a\) mandarins which were priced at \(x\) rupees each. He then decides to buy three times that number of apples. The price of an apple is twice the price of a mandarin. The fruit seller states that if the number of apples that are bought is increased by 5 fruits, he can reduce the price of each apple that is bought by 3 rupees. Accordingly, the child decides to buy 5 more apples. If he does this, write down the number of apples he buys in terms of \(a\).
|
\(3a + 5\) |
A child bought \(a\) mandarins which were priced at \(x\) rupees each. He then decides to buy three times that number of apples. The price of an apple is twice the price of a mandarin. The fruit seller states that if the number of apples that are bought is increased by 5 fruits, he can reduce the price of each apple that is bought by 3 rupees. Accordingly, the child decides to buy 5 more apples.
Write down the price of an apple in terms of \(x\).
|
\(2x - 3\) |
A child bought \(a\) mandarins which were priced at \(x\) rupees each. He then decides to buy three times that number of apples. The price of an apple is twice the price of a mandarin. The fruit seller states that if the number of apples that are bought is increased by 5 fruits, he can reduce the price of each apple that is bought by 3 rupees. Accordingly, the child decides to buy 5 more apples.
Write down the cost of the apples in terms of \(a\) and \(x\).
|
\((3a + 5)(2x - 3)\) |
A child bought \(a\) mandarins which were priced at \(x\) rupees each. He then decides to buy three times that number of apples. The price of an apple is twice the price of a mandarin. The fruit seller states that if the number of apples that are bought is increased by 5 fruits, he can reduce the price of each apple that is bought by 3 rupees. Accordingly, the child decides to buy 5 more apples.
Expand and simplify the binomial expression \((3a + 5)(2x - 3)\).
|
\(6ax - 9a + 10x - 15\) |
A certain number is denoted by \( x \). The product of the expression obtained by adding a certain number to \( x \), and the expression obtained by subtracting a different number from \( x \) is given by the expression \( x^2 + x - 56 \). Find the factors of the given expression.
|
\((x + 8)(x - 7)\) |
A certain number is denoted by \( x \). The product of the expression obtained by adding a certain number to \( x \), and the expression obtained by subtracting a different number from \( x \) is given by the expression \( x^2 + x - 56 \). What is the number that has been added to the number denoted by \( x \)?
|
8 |
A certain number is denoted by \( x \). The product of the expression obtained by adding a certain number to \( x \), and the expression obtained by subtracting a different number from \( x \) is given by the expression \( x^2 + x - 56 \). What is the number that has been subtracted from the number denoted by \( x \)?
|
7 |
The daily income earned by a vehicle used in a taxi service is Rs 8000, while the daily cost incurred by it is Rs 4500. Write the ratio of the daily income to the daily cost in its simplest form.
|
16:9 |
In a certain scale diagram, an actual distance of 1000 m is represented by 2 cm. Express this scale as a ratio.
|
1:50000 |
The gravitational force on earth is six times the gravitational force on the moon. Therefore, the ratio of the weight of an object on the moon to the weight of the object on earth is \(1 : 6\). How much would the weight of an astronaut be on the moon, if his weight on earth is 540 N.
|
90 N |
To make a cement mixture, cement and sand are mixed together in the ratio 1 : 6. What would be the fraction of cement in such a mixture?
|
\(\frac{1}{7}\) |
To make a cement mixture, cement and sand are mixed together in the ratio 1 : 6. How many pans of cement are required for 18 pans of sand?
|
3 pans |
To make a cement mixture, cement and sand are mixed together in the ratio 1 : 6. A certain bag of cement contains 5 pans of cement. If it is necessary to make a cement mixture using the whole bag, how many pans of sand are required?
|
30 pans |
To make a cement mixture, cement and sand are mixed together in the ratio 1 : 6. Find separately the number of pans of cement and the number of pans of sand that are required to make 70 pans of the cement mixture.
|
Cement: 10 pans, Sand: 60 pans |
It takes 8 men 9 days to complete a certain task. How many days will it take one man to complete the same task?
|
72 days |
It takes 8 men 9 days to complete a certain task. What is the magnitude of the task in man days?
|
72 man days |
It takes 8 men 9 days to complete a certain task. If 12 men are assigned the task, how many days will it take them to complete the task?
|
6 days |
A land owner estimates that it would take 10 men 8 days to clear his land. What is the magnitude of the task in man days?
|
80 man days |
A land owner estimates that it would take 10 men 8 days to clear his land. He hires 12 men for the initial two days. How much of the task will be completed during the first two days?
|
24 man days |
A land owner estimates that it would take 10 men 8 days to clear his land. He hires 12 men for the initial two days. If the landowner wishes to get the task done in 6 days, how many more men should he employ for the next four days?
|
2 men |
In a certain farm there was sufficient food for 12 cattle for 10 days. For how many days is the food in the farm sufficient for one of the cattle?
|
120 days |
In a certain farm there was sufficient food for 12 cattle for 10 days. After two days another four cattle were bought and brought to the farm. What is the reduction in the number of days for which the food is sufficient, due to the increase in the number of cattle?
|
2 days |
A particular tank of water can be emptied in four hours using three equal pumps. The three pumps were used to empty the tank. However, one pump stopped working after an hour. Thereafter, the tank was emptied using the other two pumps. Find how much more time was required to empty the tank due to breakdown of one pump.
|
1.5 hour |
It takes half an hour for a certain vehicle travelling at a speed of 40 kmh\(^{-1}\) to complete a certain journey. Find the time in minutes that it would take the vehicle to complete the same journey, if it travels at a speed of 50 kmh\(^{-1}\).
|
24 minutes |
Four men who were given the responsibility of completing a task were able to finish only \(\frac{2}{3}\) of it by working 6 hours a day for 3 days. What is the magnitude of the task in man hours?
|
108 man hours |
Four men who were given the responsibility of completing a task were able to finish only \(\frac{2}{3}\) of it by working 6 hours a day for 3 days. The four men decide to complete the task on the next day. How many hours will they have to work to achieve this?
|
9 hours |
It was necessary to engage 9 men for 4 days, at 5 hours per day to clear a certain land. How many men working 6 hours per day can complete the same task in 10 days?
|
3 men |
A certain task can be completed in 6 days by 18 men. It is expected to complete another task which is twice the size of the initial task in 9 days. Find how many men are required to complete the second task in 9 days.
|
24 men |
An ice-cream producing company has three ice-cream vans. The three vans arrive at the housing complex “Isuruvimana” once every 3 days, once every 6 days, and once every 8 days respectively. If all three vans arrived at “Isuruvimana” on a certain day, after how many days will they all arrive at this housing scheme again on the same day?
|
24 days |
Mr. Gunatillake visits Galle Face grounds every Sunday evening to observe the setting of the sun. Mr. Mohamed and Mr. Perera too visit the same location once every 6 days and once every 8 days respectively for the same reason. If the three of them met each other for the first time in Galle Face grounds on Sunday the 8th of December 2013, after how many days did they all meet each other again at the same location? On which date did they meet again?
|
24 days, January 1, 2014 |
Simplify the expression \(\frac{x+3}{x^2-1} + \frac{1}{x+1}\).
|
\(\frac{2}{x-1}\) |
Simplify the expression \(\frac{t-1}{t+1} + \frac{1}{t^2-1}\).
|
\(\frac{t^2 - t + 1}{(t+1)(t-1)}\) |
Simplify the expression \(\frac{1}{x+1} + \frac{1}{(x+1)^2} + \frac{1}{x^2-1}\).
|
\(\frac{2x + 3}{(x+1)^2(x-1)}\) |
Simplify the expression \(\frac{1}{a-3} + \frac{1}{a^2-a-6}\).
|
\(\frac{a + 2}{(a-3)(a+2)}\) |
Simplify the expression \(\frac{1}{x+3} + \frac{1}{x^2+x-6}\).
|
\(\frac{x - 1}{(x+3)(x-2)}\) |
Simplify the expression \(\frac{3}{x^2+x-2} - \frac{1}{x^2-x-6}\).
|
\(\frac{2x + 11}{(x+2)(x-1)(x-3)}\) |
Simplify the expression \(\frac{4}{p^2+p-6} - \frac{2}{p^2+5p+6}\).
|
\(\frac{2p + 10}{(p+3)(p-2)(p+2)}\) |
Simplify the expression \(\frac{1}{x^2+4x+4} - (x-2)(x+2)\).
|
\(\frac{-x^3 - 4x^2 - 4x + 1}{(x+2)^2}\) |
Simplify the expression \(\frac{3}{a^2+5a+6} + \frac{1}{a^2+4a+3}\).
|
\(\frac{4a + 10}{(a+2)(a+3)(a+1)}\) |
Simplify the expression \(\frac{1}{2a+1} + \frac{1}{a^2+3a+2}\).
|
\(\frac{a^2 + 5a + 3}{(2a+1)(a+1)(a+2)}\) |
A father and his sons equally shared an amount of Rs 270. Then the amount each person had was Rs 45. Taking the number of sons as \( x \), construct an equation. Solve this equation and hence find the number of sons the father has.
|
5 |
When the same number was added both to the numerator and the denominator of the fraction \( \frac{3}{5} \), the resulting fraction was equal to \( \frac{9}{10} \). What number was added?
|
15 |
The price of two baby shirts and three pairs of baby shorts is Rs. 1150. Three baby shirts and a pair of baby shorts cost Rs. 850. Taking the price of a baby shirt as Rs. \( x \) and that of a pair of baby shorts as Rs. \( y \), construct two simultaneous equations and find the price of a baby shirt and that of a pair of baby shorts separately by solving the two equations.
|
\( x = 200 \), \( y = 250 \) |
Dinithi’s father tells Dinithi, “My age is now four times your age. 8 years earlier, I was twelve times older than you.” Find the present ages of the father and Dinithi separately.
|
Father: 44 years, Dinithi: 11 years |
A cylindrical water tank of cross-sectional area 0.5 m\(^2\) is filled to a height of 70 cm in 1 minute and 10 seconds by a pipe through which water flows at a uniform rate. Calculate the rate at which water flows out of the pipe.
|
0.005 m\(^3\)/s |
The distance between railway stations \( X \) and \( Y \) is 420 km. A train leaves station \( X \) at 7.00 p.m. and travels towards station \( Y \) with a uniform speed of 100 kmh\(^{-1}\). An hour later, another train leaves station \( Y \) and travels towards station \( X \) with a uniform speed of 60 kmh\(^{-1}\). At what time do the two trains pass each other?
|
10:00 p.m. |
The railway stations \( A \) and \( B \) are 300 km apart. A certain train takes 12 hours to travel from \( A \) to \( B \) and then back to \( A \), after spending 2 hours at \( B \). Another train leaves station \( A \) ten hours after the first train left \( A \), and travels towards \( B \) at the same uniform speed. How far has the second train travelled when the two trains pass each other?
|
100 km |
The energy that a moving object possesses is given by the formula \(E = mgh + \frac{1}{2}mv^2\). Express the mass of the object in terms of the other quantities.
|
\( m = \frac{E}{gh + \frac{1}{2}v^2} \) |
The energy that a moving object possesses is given by the formula \(E = mgh + \frac{1}{2}mv^2\). Express the velocity of the object in terms of the other quantities.
|
\( v = \sqrt{\frac{2(E - mgh)}{m}} \) |
The energy possessed by an object of mass 3 kg when it is 5 m above the ground is 153 N. Find the velocity of this object at this moment. Take \( g = 10 \, \text{ms}^{-1} \).
|
1.41 m/s |
Rs. 100 is sufficient to buy 3 mangoes and 2 mandarins. If the price of a mango is Rs. 20 and the price of a mandarin is taken to be Rs. \( y \), then an inequality \( 60 + 2y \leq 100 \) in \( y \) can be written. Solve this inequality and find the maximum value that the price of a mandarin can take.
|
20 |
Nimal placed a 1 kg standard weight in one pan of a balance scale and a 500 g standard weight and three cakes of soap of the same type on the other pan. He observed that the pan with the 1 kg standard weight dipped below the other pan. If the mass of a cake of soap is taken as \( p \) grammes, an inequality \( 1000 > 500 + 3p \) in terms of \( p \) can be written. Find the maximum integral value that the mass of a cake of soap can be.
|
166 |
Simplify the expression \(\frac{5}{x} \times \frac{10}{x}\).
|
\(\frac{50}{x^2}\) |
Simplify the expression \(\frac{m}{3n} \div \frac{m}{2n^2}\).
|
\(\frac{2n}{3}\) |
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