Ratios - Solved Examples

Q 1 - On the off chance that a:b=2:3 and b:c=5:7, discover a:c.
A - 10:11
B - 10:21
C - 21:10
D - 11:10
Answer - B
Explanation
We have a/b = 2/3 and b/c = 5/7 
So a/c = (a/b*b/c) = (2/3*5/7) = 10/21 
So its demonstrate that a:c = 10:21

Q 2 - On the off chance that a:b=2:3 and b:c=5:7, discover a:b:c.
A - 10:15:21
B - 10:21:15
C - 15:10:21
D - 11:10:21
Answer - A
Explanation
Here a/b = 2/3 and b/c = 5:7 = 3/5*5:3/5*7 = 3:21/5. 
So a:b=2:3 and b:c=3:21/5 
So a:b:c = 2:3:21/5 = 10:15:21. 

Q 3 - On the off chance that 4a = 5b and 8b = 9c, find a:b:c.
A - 45:36:32
B - 45:32:36
C - 32:45:36
D - 32:36:45
Answer - A
Explanation
4a = 5b
=> a/b=5/4
and 8b = 9c
=> b/c=9/8 
So a:b = 5:4 and b:c = 9:8 = (4/9)(9):(4/9)(8) = 4:32/9 
=> a:b:c = 5:4:32/9 = 45:36:32. 
Hence,a:b:c = 45:36:32. 

Q 4 - On the off chance that a/8 = b/9 = c/12, find a:b:c.
A - 8:12:9
B - 8:9:12
C - 12:8:12
D - 9:8:12
Answer - B
Explanation
Let a/8 = b/9 =c/12 =k. 
Then a=8k ,b=9k and c=12k. 
So a:b:c = 8k:9k:12k =8:9:12. 
Hence,a:b:c = 8:9:12.

Q 5 - In the event that a:b =1:3, b:c = 5:7 and c:d = 9:8 ,find a:b:c:d.
A - 45:15:63:56 
B - 63:45:15:56 
C - 15:45:63:56 
D - 15:63:45:56 
Answer - C
Explanation
We have a:b = 1:3, b:c = 5:7 and c:d = 9:8 
=> a:b = 5:15, b:c = 15:21, c:d =(21/9)*9 : (21/9)*8 
=> a:b = 5:15, b:c = 15:21, c:d = 21:56/3  
=> a:b:c:d =5:15:21:56/3 = 15:45:63:56 
Consequently, a:b:c:d = 15:45:63:56 

Q 6 - In the event that (5x+3y): (5x-3y) =3:1, then x:y=?
A - 6:5 
B - 7:8 
C - 8:9 
D - 9:11 
Answer - A
Explanation
Here (5x+3y)/(5x-3y) = 3/1  
=> 5x+3y = 15x-9y
=> 10x = 12y
=> x/y = 12/10 = 6/5 
So x:y =6:5 

Q 7 - In the event that x:y= 5:3 ,then ( 8x-5y) : (8x+5y) = ?
A - 6:11 
B - 7:11 
C - 8:11 
D - 5:11 
Answer - D
Explanation
Given x/y = 5/3 
Dividing numerator and denominator by y.
(8x-5y)/(8x+5y) = {8(x/y) - 5}/{8(x/y) + 5}
= {8*(5/3)-5}/{8*(5/3)+5}
= (40-15)/(40+15)
= 25/55
= 5/11 
So (8x-5y):(8x+5y)= 5:11

Q 8 - locate the fourth corresponding to 4,5 and 12.
A - 18 
B - 16 
C - 14 
D - 15 
Answer - D
Explanation
Let 4:5::12:x. 
=> 4*x = (5*12) 
=> x = 5*12/4
= 15 
So the fourth relative to 4,5,12 is 15. 

Q 9 - locate the third proportinal corresponding to 9 and 12.
A - 18 
B - 16 
C - 14 
D - 15 
Answer - B
Explanation
Third relative to 9 and 12 is equivalent to fourth corresponding to 9,12 and 12. 
Give it a chance to be x at that point 
=> 9:12::12:x 
=> 9x = 12*12 
=> x = 12*12/9
=16 
So the third relative is 16. 

Q 10 - Locate the mean relative somewhere around 49 and 64.
A - 58 
B - 56 
C - 54 
D - 55 
Answer - B
Explanation
Mean relative somewhere around 49 and 64 is 49*64 = (7*8) = 56. 

Q 11 - An aggregate of rs. 391 has been divided between a,b,c in the proportion 1/2 :2/3:3/4 , discover the offer of each.
A - 102,136,153 
B - 112,114,123 
C - 114,117,129 
D - 122,134,123 
Answer - A
Explanation
We have a:b:c=1/2:2/3:3/4= 6:8:9. 
A share = (391*6/23) = 102 rs. 
B offer = (391*8/23) = 136 rs. 
C offer = (391*9/23) = 153 rs.

Q 12 - A sack contain one rupee, fifty paisa and 25 paisa in the proportion of 8:9:11, if the aggregate cash of the pack is 122, discover the no. of coins of every sorts.
A - 8,64,72,88 
B - 16,32,72,88 
C - 8,64,128,88 
D - 32,64,128,88 
Answer - A
Explanation
Let the quantity of one rupee, 50-p and 25-p coins be 8x, 9x and 11x individually. 
At that point, 8x + 9x/2 + 11x/4 =122 
=> 32x + 18x + 11x = 488
=> 61x =488 
=> x = 8 
No. of one rupee coins = 8*8= 64 
No. of 50-p coins =9*8= 72 
No. of 25-p coins =11*8 =88 

Q 13 - A blend contains liquor and water in the proportion 4:3, if 7 liter of water is added to the blend, the proportion of liquor and water gets to be 3:4. Discover the amount of liquor in the blend. 
A - 12 liters 
B - 13 liters 
C - 14 liters 
D - 15 liters 
Answer - B
Explanation
Let the amount of liquor and water be 4x liter and 3x liter separately.
At that point , 4x/3x + 7 = 3/4 
=> 16x = 9x+21 
=> 7x = 21 
so estimation of x is 3 
Amount of liquor in the blend is = 4*3 =12 liters. 

Q 14 - In a collection, the no. of understudy considering expressions, trade and science in the proportion of 4:7:9. On the off chance that the no. of understudy in expressions of the human experience, business and science be expanded by 30%, 20% and 40%. What will be the new proportion? 
A - 26:42:63 
B - 36:42:63
C - 46:42:63 
D - 56:42:63 
Answer - A
Explanation
Let the no. of understudy in expressions, business and science be 4x,7x and 9x individually. 
Presently they are 130% of 4x, 120 % of 7x and 140 % of 9x. 
Required proportion = (130/100*4x): (120/100*7x) (140/100*9x) 
=26x/5:42x/5:63x/5
=26:42:63.

Q 15 - The expense of assembling an auto is comprised of three items: cost of material, work and overheads. In a year, the expense of these things were in the proportion 4:3:2.Next year, the expense of material rose by 10%,cost of work expanded by 8% however the overheads lessened by 5%.Find the increment for every penny in the auto's cost.
A - 44/9 %  
B - 54/9 % 
C - 64/9 % 
D - 74/9 %  
Answer - A
Explanation
Let the expense of material, work and over head be rs. 4x, 3x and 2x separately. 
At that point aggregate expense =9x rs . 
New cost= {(110% of 4x) + (108% of 3x) +(90% of 2x)} 
={(110/100*4x)+(108/100*3x)+(90/100*2x)} 
= (22x/5 + 81x/25 + 9x/5)
= (110x+81x+45x)/25= 236x/25 
Increment = {(236x/25)-9x} = 11x/25 
Increase%= (11x/25)*(1/9x)*100 % 
= 44/9 % 

Q 16 - The proportion of no. of young men to that of the young ladies in a school is 3:2 .if 20% of young men and 25% of young ladies are grant holders, discover the % of the individuals who are not grant holders.
A - 64 %  
B - 78 % 
C - 84 % 
D - 76 %  
Answer - B
Explanation
Let the no. of young men be 3x and the no. of young ladies 2x. 
Aggregate no. = 5x 
No. of the individuals who are not grant holders 
= (80% of 3x)+(75% of 2x) 
= (80/100 * 3x) + ( 75/100 * 2x) 
= (12x/5 + 3x/2)
= 39x/10 
Required % = (39x/10)*(1/5x)*100 %
= 78% 

Q 17 - An and B together have rs.1210 with them. In the event that 4/15 of A sum is equivalent to 2/5 of B sum, what amount of sum does B have? 
A - 484  
B - 284 
C - 384 
D - 584  
Answer - A
Explanation
Let (4/15)a = (2/5)b = x 
then a = 15x/4 and b = 5x/2 
So. 15x/4 + 5x/2 =1210 
=> 15x + 10x = 4840 
=> 25x = 4840 
=> x=193.6 
So. B = (5/2*193.6) = 484 
Henceforth B has Rs. 484.

Q 18 - In the event that (x+y): (x-y)= 4:1,then (x2+y2): (x2-y2)=? 
A - 17/8  
B - 19/8 
C - 15/8 
D - 13/8  
Answer - A
Explanation
(x + y)/(x - y)= 4/1
=> x + y = 4x-4y
=> 3x = 5y
=> x/y = 5/3
Now (x2+y2)/ (x2-y2)=  {(x/y)2+1}/ { (x/y )2-1 }
= {(5/3)2+1} / {(5/2)2 -1} 
= 34/16 = 17/8 

Q 19 - In the event that (4x2-3y2) :( 2x2+5y2)= 12:19 , then x:y=? 
A - 2:1  
B - 3:2 
C - 4:1 
D - 5:2  
Answer - B
Explanation
(4x2 -3y2)/ (2x2 +5y2) = 12/19
=>76x2-57y2 = 24x2+60y2
=> 52x2 = 117y2
=> x2/y2 = 117/52 = 9/4
=> (x/y)2=(3/2)2
=> x/y = 3/2.
=> x:y = 3:2

Q 20 - if x2+y2 = 4xy,then x:y = ? 
A - 2:1  
B - 3:2 
C - 4:1 
D - 5:2  
Answer - A
Explanation
As x2+4y2 = 4xy 
=> x2 + 4y2 - 4xy = 0 
=> (x-2y)2 = 0
=> x-2y=0 
=> x = 2y 
=> x/y = 2/1.
=> x:y = 2:1.


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