MU-NLPC/Calc-aqua_rat huggingface dataset:
If a number is exactly divisible by 11 and 13, which of the following types the number must be?
Choose the correct choice from the following answers:	A) Divisible by (11 + 13)	B) Divisible by (13 - 11)	C) Divisible by (11 x 13)	D) Divisible by (13 ÷ 11)	E) None

Solution: Answer   LCM of 11 and 13 will be (11 x 13). Hence, if a number is exactly divisible by 11 x 13, then the same number must be exactly divisible by their LCM or by (11 x 13).   Divisible by (11 x 13)orrect Option: Divisible by (11 x 13)
Answer: C
A dance delegation of 4 people must be chosen from 5 pairs of dance partners. If 2 dance partners can never be together on the delegation, how many different ways are there to form the delegation?  Choose one:
A) 20
B) 30
C) 60
D) 70
E) 80

Solution: Since 2 dance partners can never be together, lets select 4 pairs from 5 pairs of dance partners to fill the 4 positions. Now, in each position, each pair can be selected in 2 different ways.   Therefore number of ways of forming a delegation such that the 2 dance partners are never together = 5C4*(2C1)^4 = 5 * 16= 
5 * 16 = 80
80   Answer: 80
Answer: E
If x = 1- 2t and y = 2t - 2, then for what value of t does x = y?
Choose the correct choice:
A) 5/2  B) 3/2  C) 3/4  D) 2/5  E) 0

Solution: We are given x = 1 – 2t and y = 2t – 2, and we need to determine the value for t when x = y. We should notice that both x and y are already in terms of t. Thus, we can substitute 1 – 2t for x and 2t – 2 for y in the equation x = y. This gives us:   1 – 2t = 2t – 2   3 = 4t   3/4 = t   The answer is 3/4.
Answer: C
If x and y are positive integers, and 4x^2=2y, then which of the following must be a multiple of 9?
I. x^2
II. y^2
III. xy	Choices.
A) I only B) II only C) III only D) I and II only E) I, II and III

Solution: 4x^2 = 3y   since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2   -> x^2 and y is divisible by 9 -> y^2 is divisible by 9   (1),(2), and (3) must be true   Answer is II only
Answer: B
The average (arithmetic mean) of 20, 40, and 60 is 8 more than the average of 10, 70, and what number?
Choose the correct choice
A) 16 B) 25 C) 35 D) 45 E) 55

Solution: a1 = 120/3= 
120/3 = 40
40   a2= a1 -8 = 32   sum of second list = 32*3= 
32*3 = 96
96   therefore the number= 96 -80= 
96 -80 = 16
16   16NSWER:16
Answer: A
Anil had to do a multiplication. Instead of taking 35 as one of the multipliers, he took 53. As a result, the product went up by 540. What is the new product? Choose the correct choice from the following answers:
A) 1590  B) 1600  C) 1950  D) 1630  E) 1760

Solution: Explanation :   Let the number that Anil wanted to multiply be 'Y'.   He was expected to find the value of 35Y.   Instead, he found the value of 53Y.   The difference between the value that he got (53Y) and what he was expected to get (35Y) is 540.   => 53Y - 35Y = 540   => (53 - 35) * Y = 540   => Y = 30   Therefore, the correct product = 53 * 30= 
53 * 30 = 1_590
1590   1590nswer : 1590
Answer: A
Murali travelled from city A to city B at a speed of 50 kmph and from city B to city C at 50 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?	Choose one:
A) kmph
B) kmph
C) kmph
D) kmph
E) kmph

Solution: Let the distances between city A to B and B to C be 2x km and 3x km respectively.   Total time taken to cover from A to C   = (2x)/50 + (3x)/50   = (2x + 3x)/50 = 5x/100   = x/20 Average speed   = (2x + 3x)/(x/20) = 100 kmph.   Answer: kmph
Answer: B
A city council will select 2 of 9 available firefighters and 1 of 4 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel? Choose one:
A) 36
B) 72
C) 144
D) 216
E) 432

Solution: OA D   91442 * 41441   using the combination formula to choose 2 from 9 and 1 from 4   144
Answer: C
you need to pict any number from 1, 3,5,7,9,11,13 and 15 to make below equation true.
()+()+()=30
can you solve it?	Choose the correct choice from the following answers:	A) 7+15+9	B) 6+15+9	C) 6+14+9	D) 6+15+8	E) 8+15+9

Solution: Correct Answer : 6+15+9   3x+15+9=30   3x =3*2*1= 
3*2*1 = 6
6   therefore :- 6+15+9= 30
Answer: B
A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum Z of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?  Select
A) 5	B) 7	C) 9	D) 10	E) 14

Solution: Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum Z of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is 10, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.10
Answer: D
If $0.80 is the commission for sales of $2,000, what percent of the sales amount is the commission?  Choose the correct choice from the following answers:
A) 4%
B) 0.4%
C) 0.04%
D) 0.004%
E) 0.0004%

Solution: % of sales amount of commission   = (0.04%ommission/Total Value) *100   = (0.8/2000) * 100= 
(0.8/2000) * 100 = 0.04
0.04%   The answer is 0.04%.
Answer: C
A bookseller sells his books at a 10% markup in price. If he sells a book for $11.00, how much did he pay for it?	Choose the correct choice from the following answers:
A) $14.40	B) $14.00	C) $10.00	D) $9.60	E) $5.00

Solution: Let the cost price of book = x   Selling price of book = 11$   Markup % = 10   (110/100)x = 11   => x = 10   Answer $10.00
Answer: C
Which of the following could be the sides of an obtuse angled triangle? all values are in degree
I. 19, 29, 39
II. 29, 39, 49
III. 10,110, 60	Choose the correct choice from the following options:
A) III only
B) II only
C) III only
D) I and II only
E) I, II and III

Solution: obtuse angled triangle means one angle more than 90deg and total 180 deg.. III   III only
Answer: A
With what number must 6.2587 be multiplied in order to obtain the number 625.87?	Choose the correct choice from the following.
A) 1000  B) 1,0000  C) 100  D) 100,000  E) None of these

Solution: Explanation: The decimal must be moved two places to the right. To do this, we must multiply by a number with two zeroes. The correct answer is 100.The decimal must be moved two places to the right. To do this, we must multiply by a number with two zeroes. The correct answer is 100.   Answer : (100)
Answer: C
Students of three different classes appeared in common examination. Pass average of 10 students of first class was 60%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?	Choose one: A) 74% B) 75% C) 69% D) 70% E) None

Solution: Solution:   Sum of pass students of first, second and third class,   = (60% of 10) + (60% of 15)+ (80% of 25)   = 6+9+20= 
6+9+20 = 35
35   Total students appeared,= 10+15+25= 
10+15+25 = 50
50   Pass average,= 35*100/50= 
35*100/50 = 70
70%.   Answer: Option 70%
Answer: D
A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour?
Choose the most appropriate option:
A) 7 km/hr  B) 7.2 km/hr  C) 7.4 km/hr  D) 7.8 km/hr  E) 8.9 km/hr

Solution: Speed = 600 m/sec.   5 x 60   = 2 m/sec.   Converting m/sec to km/hr (see important formulas section)   = 2 x 18 km/hr   5   = 7.2 km/hr   7.2 km/hr
Answer: B
Which of the following inequalities is always true for any non-negative real numbers numbers 'x' and 'y'?	Choose the most appropriate option.
A) (x-y)^2 >= x^2 + y^2	B) (x+y)^2 <= x^2 + y^2	C) (x+y)^2 = x^2 + y^2	D) (x+y)^2 <= x^2 + y^2	E) (x+y)^2 >= x^2 + y^2

Solution: Using the concept of superadditivity, we know that for non-negative real numbers the square of the sum of x and y will always be more than the sums of x and y separately; this is a superadditive function. Therefore the answer is (x+y)^2 >= x^2 + y^2.
Answer: E
In a certain sequence, the first term is 2, and each successive term is 2 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?
Choose the correct choice from the following answers
A) 13/8  B) 21/13  C) 58/5  D) 70/29  E) 82/13

Solution: let five terms in the sequence be a,b,c,d,e   a=2   b= 2+1/2=5/2   c=2+2/5= 12/5   d= 2+5/12 = 29/12   e= 2+12/29 = 70/29   hence answer should be 70/29.
Answer: D
Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 74 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad? Answers
A) 3
B) 4
C) 5
D) 6
E) 8

Solution: Total Distance = 74 kms   Maxwell Speed = 4 kms/hr   Maxwell travelled for 1hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.   Time taken = Total Distance / Relative Speed   Total Distance after Brad started = 70 kms   Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4= 
6+ 4 = 10
10 kms/hr   Time taken to meet Brad after Brad Started= 70 / 10= 
70 / 10 = 7
7 hrs   Distance traveled by Maxwell= Maxwell's speed * time taken = 4 * 7= 
4 * 7 = 28
28+4= 
28+4 = 32
32 kms...   Therefore Total Time taken by Maxwell to meet Brad= Distance travelled by Maxwell / Maxwell's Speed = 32 /4= 
32 /4 = 8
8 hrs ... Answer 8
Answer: E
The number of roots common between the two equations x3 + 3x2 + 4x + 5 = 0 and x3 + 2x2 + 7x + 3 = 0 is  Choices
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Explanation :   Let α is the common root.   ∴ α3 + 3α2 + 4α + 5 = 0. ............................(i)   α3 + 2α2 + 7α + 3 = 0. .............................(ii)   On subtracting (ii) from (i), we get   α2 - 3α + 2 = 0.   α = 2, α = 1.   But the above values of α do not satisfy any of the equations. Thus, no root is common.   0nswer : 0
Answer: A
If 4XZ + YW = 4 and XW + YZ = 8, what is the value of the expression (2X + Y)(2Z + W)?	Choose the correct choice:  A) 22  B) 20  C) 24  D) 26  E) 28

Solution: (2x+y)*(2z+w) = 4+2(8) =20   Answer : 20
Answer: B
B completes a work in 7 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?	Choices:
A) 3.75 days	B) 4.11 days	C) 5.11days	D) 6.75 days	E) 7.33 days

Solution: 1/7 + 1/10 = 17/70   70/17 = 4.11 days   ANSWER:4.11 days
Answer: B
In one hour, a boat goes 8 km along the stream and 2 km against the stream. the sped of the boat in still water (in km/hr) is :	Pick:
A) 3 B) 5 C) 8 D) 9 E) 10

Solution: Solution   Speed in still water= 1/2(8+2) km/hr= 5kmph. Answer 5
Answer: B
If x/4 + 24/x = 5, what are the values of 2x - 7?  Choose the most appropriate option:	A) 8 and 9	B) 8 and 24	C) 17 and 21	D) 12 and 29	E) 17 and 9

Solution: I got the same thing 17 and 9 is the answer 9 or 17
Answer: E
There are three departments having students 62,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required? Select the correct option:  A) 72  B) 74  C) 75  D) 76  E) 77

Solution: WE NEED TO TAKE GCD WHICH IS 2   THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT   1) 62/2 = 31   2) 58/2 = 29   3) 24/2 = 12   TOTAL NO. OF MIN ROOMS REQD = 31+12+29= 
31+12+29 = 72
72   72NSWER:72
Answer: A
On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 350 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
Pick.
A) 237  B) 287  C) 197  D) 287  E) 700

Solution: Explanation:   Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.   2x/(x - 350) = 2 + 2(extra)   => 2x - 700 = x => x = 700.   Answer: 700
Answer: E
P runs 25% faster than Q so P gives Q a 60 meter head start. If the race ends in a tie, how far (in meters) did P run in the race?	Choose the correct choice from the following options:
A) 100	B) 200	C) 300	D) 400	E) 500

Solution: Let D be the race distance that P ran.   Let T be the time it took to complete the race.   Let V be Q's speed.   T = D/1.25V = (D-60) / V   D=1.25D-75   0.25D=75   D=300 meters.   The answer is 300.
Answer: C
Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64500. What is his profit percent?  Choose the correct choice:	A) 22	B) 77	C) 17.3	D) 99	E) 88

Solution: Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64500   Profit(%) = (64500 - 55000)/55000 * 100 = 17.3%   Answer: 17.3
Answer: C
Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Select the correct option:  A) 5  B) 2  C) 9  D) 5  E) 1

Solution: 1250   = D(100/4)2   D = 2   Answer: 2
Answer: B
Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3? Choose the correct option:  A) 0  B) 1  C) 2  D) 3  E) 4

Solution: For: (2^(3x+3)+3)/3   Let n = 3x + 3   2^n   2^1 = 2   2^2 = 4   2^3 = 8   2^4 = 16   2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, ....   Rule: x^(m+n) = (x^m)(x^n)   (2^(3x))(2^3)   Rule: x^(mn) = (x^m)^n   ((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1.   Answer: 1
Answer: B
A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party W. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
Choose the correct choice from the following answers
A) 15	B) 20	C) 30	D) 35	E) 45

Solution: S=100   not( W and B ) =35   only W=20   (W and B)/B=1/2   let ( W and B ) =x   only B =2x   so now, 20+35+x+2x=100   x= 15   15 ans
Answer: A
If x < y < z and y-x > 11, where x is an even integer and y and z are odd integers, what is the least possible value of z - x? Choose the correct choice from the following options
A) 6  B) 7  C) 8  D) 9  E) 15

Solution: We have:   1) x<y<z 2)="" y-x="">11   3) x</y<z>=2k (x is an even number)   4) y=2n+1 (y is an odd number)   5) z=2p+1 (z is an odd number)   6) z-x=? least value   z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number.   we are asked to find the least value, so we have to pick the least numbers   since y is odd and x is even, y-x must be odd. since y-x>11, the least value for y-x must be 13, the least value for x must be 2, and, thus, the least possible value for y must be 15 (y-2=13, y=15)   2<15<z, since z is odd, the least possible value for z is 17   z-x=17-2= 
17-2 = 15
15   Answer 15
Answer: E
The profit obtained by selling an article for Rs. 66 is the same as the loss obtained by selling it for Rs. 22. What is the cost price of the article?  Choose the correct choice from the following choices:
A) Rs. 40
B) Rs. 50
C) Rs. 49
D) Rs. 59
E) Rs.44

Solution: S.P 1- C.P = C.P – S.P 2   66 - C.P = C.P - 22   2 C.P = 66 + 22;   C.P = 88/2= 
88/2 = 44
44   ANSWRs.44R:Rs.44
Answer: E
If 25% of a number is equal to one-third of another number, what is the ratio of first number to the second number?	Options:
A) 4:3 B) 1:4 C) 3:7 D) 6:11 E) 2:3

Solution: Let 25% of 4:3 = 1/3 B   then 254:3/100 = 1B/3   4:3/4 = B/3   4:3/B = 4/3   4:3:B = 4:3   4:3nswer is 4:3
Answer: A
A pupil's marks were wrongly entered as 73 instead of 40. Due to the average marks for the class got increased by half. The number of pupils in the class is?	Choose the correct choice from the following choices
A) 18	B) 82	C) 66	D) 27	E) 77

Solution: Let there be x pupils in the class.   Total increase in marks   = (x * 1/2) = x/2   x/2 = (73 - 40) => x/2   = 33 => x = 66.   Answer: 66
Answer: C
On a scale that measures the intensity of a certain phenomenon, a reading of a+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of a. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?	Pick one:
A) 5	B) 50	C) 10^5	D) 5^10	E) 8^10 - 3^10

Solution: To solve this problem we need to examine the information in the first sentence. We are told that “a reading of a + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of a.”   Let’s practice this idea with some real numbers. Let’s say a is 2. This means that a + 1 = 3. With the information we were given we can say that a reading of 3 is ten times as great as the intensity of a reading of 2.   Furthermore, we can say that a reading of 4 is actually 10 x 10 = 10^2 times as great as the intensity of a reading of 2.   Increasing one more unit, we can say that a reading of 5 is 10 x 10 x 10 = 10^3 times as great as the intensity of a reading of 2.   We have found a pattern, which can be applied to the problem presented in the stem:   3 is “one” unit away from 2, and thus a reading of 3 is 10^1 times as great as the intensity of a reading of 2.   4 is “two” units away from 2, and thus a reading of 4 is 10^2 times as great as the intensity of a reading of 2.   5 is “three” units away from 2, and thus a reading of 5 is 10^3 times as great as the intensity of a measure of 2.   We can use this pattern to easily answer the question. Here we are being asked for the number of times the intensity corresponding to a reading of 8 is as great as the intensity corresponding to a reading of 3. Because 8 is 5 units greater than 3, a reading of 8 is 10^5 times as great as the intensity corresponding to a reading of 3.   Answer 10^5.
Answer: C
Two family reunions are happening at the same hotel, the Oates reunion and the Yellow reunion. All 100 guests at the hotel attend at least one of the reunions. If 42 people attend the Oates reunion and 65 people attend the Yellow reunion, how many people attend both reunions?  Choose the correct choice from the following:
A) 2  B) 7  C) 10  D) 16  E) 22

Solution: No of people in Oates reunion=42   No of people in Yellow reunion=65   Attending both=x   All guests attend at least one.   Therefore, 100=42+65-(7oth)   7oth=7   Answer 7
Answer: B
Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 45 days. On which day of the week in February was the task completed?  Choose the correct choice from the following options
A) Tuesday  B) Wednesday  C) Saturday  D) Sunday  E) Monday

Solution: This type of story problem is essentially just about a repeating pattern and a 'remainder.'   We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 45 DAYS. We're asked on what day of the week the task was actually completed on.   Since the task was supposed to be completed on a Wednesday....   A 1 day postponement would be Thursday   A 2 day postponement would be Friday   A 3 day postponement would be Saturday   A 4 day postponement would be Sunday   A 5 day postponement would be Monday   A 6 day postponement would be Tuesday   A 7 day postponement would be Wednesday   A 8 day postponement would be Thursday   Etc.   So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 45 days.   45/7 = 6 remainder 3   This means that there are 6 full weeks AND 3 extra days after a Wednesday....Thus, the task was completed on a Saturday.   Saturday
Answer: C
If abc = ab^3 = 180 where a, b and c are positive integers, what is the value of `c’?
Choose the correct choice from the following answers
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: abc = a(b^3) = 180   on solving abc = a(b^3) we get c = b^2   and for a(b^3) = 180 , there is only one possibility a = 180 and b = 1 so c = 1^2 = 1   ANSWER:1
Answer: B
Find the number of ways in which 8064 can be resolved as the product of two factors?
Choose the correct choice from the following:  A) 22  B) 24  C) 21  D) 20  E) 19

Solution: Solution:   Total number of ways in which 8064 can be resolved as the product of two factors is 24 as below:   (1,8064), (2,4032), (3,2688), (4,2016), (6,1344), (7,1152),(8,1008), (9,896), (12,672), (14,576), (16,504), (18,448), (21,884), (24,336), (28,288), (32,252), (36,224), (42,192), (48,168), (56,144), (63,128), (68,126), (72,112), (84,96).   Answer: Option 24
Answer: B
How many paying stones, each measuring 4 m * 2 m are required to pave a rectangular court yard 40 m long and 20 m board?  Options:
A) 99
B) 18
C) 100
D) 17
E) 12

Solution: 40 * 20 = 4 * 2 * x => x   = 100   Answer: 100
Answer: C
4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?	Choose one:
A) 2277
B) 2882
C) 2800
D) 2677
E) 2211

Solution: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144   3x/100 + 200 – 5x/100 = 144   2x/100 = 56 è x = 2800   Answer: 2800
Answer: C
A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 900. How many workers were part of the latter production run? Choose the correct choice from the following answers
A) A)6
B) B)10
C) C)11
D) D)15
E) E)34

Solution: The daily average production is given by 5n + 20- given   In the first k days, 500 units are produced   = (5n+20)K =500   k = 500/5n+20...................................1   5 workers were added = 5(n+5)+20 = 5n +45   cumulative is 900 .. thus for the current period = 900 -500= 
900 -500 = 400
400   (5n+45)K= 400   k = 400/5n+45........................................2   equate 1 and 2   500/5n+20 = 400 /5n+45   500(5n+45) = 400(5n+20)   25n + 225 = 20n + 80   5n =145   n = 29   thus n+5 = 34   hence 34
Answer: E
An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.18522/- in 3 years at the same rate of interest. Find the rate percentage? Choose the correct choice.
A) 5%  B) 6%  C) 7%  D) 8%  E) 9%

Solution: The difference of two successive amounts must be the simple interest in 1 year on   the lower amount of money.   S.I = 18522/- - 17640/- = Rs. 882/-   Rate of interest = (882/17640) × (100/1) => 8820/1764= 
8820/1764 = 5
5%   Principal= 5%mount/(1 + R/100)n   = 17640/(1 + 5/100)2   = 17640/(21/20 × 21/20)   = 17640/(1.05 × 1.05)   = 17640/1.1025= 
17640/1.1025 = 16_000
16000   Thus the principal is Rs.16000/- and the rate of interest is 5%   5%
Answer: A