Ratio & Proportion Questions for CAT with Answers PDF

Assume the weight of the heaviest piece = 5x
Then, the weight of the lightest piece = x
So, the weight of medium weighted piece = x + 18
∴ (5x) + (x + 18) + (x) = 60
⇒ x = 6
So, the weight of the heaviest piece = 5 × 6 = 30 grams

Assume A has x candies and B has y candies.
If he gives half to B, i.e x/2 then B will have 1.3y candies.
Thus,
0.3y = x/2

Let the amounts of water in the bottles be V, 2V, 3V, 4V, 5V and 6V.
So, total water poured = 21V
Let the capacity of each bottle be C.
So, capacity of six bottles = 6C
Capacity of jar = 3C
As the jar is completely filled, we have
21V = 3C
Or 7V = C
Now, 70% of 7V = 4.9V
Thus, there are two bottles which were at least 70% filled with water.
Hence, answer option 3 is correct.

Average of set A elements = x + 4.5
Average of set B elements = y + 7
So,  = 9/14
⇒ 14x + 63 = 9y + 63
⇒ x/y = 9/14

A gets 10% of the profit for managing the business = 10% of 9600 = Rs. 960
Profit remaining = 9600 - 960 = Rs. 8640
Ratio in which they will share the remaining profit = 12 : 20 = 3 : 5
A's share = 960 + (3/8) 8640 = Rs. 4200

Let the numbers be x, y and z.
x + y + z = 98
Also, x : y = 2 : 3 and y : z = 5 : 8
Therefore, x : y : z = 10 : 15 : 24
Let x = 10k, y = 15k and z = 24k
Then, 10k + 15k + 24k = 98 
⇒ k = 2
The numbers are 20, 30 and 48.
Hence, second number is 30.

Let (a + b) = 6k, (b + c) = 7k and (c + a) = 8k.
Then, 2 (a + b + c) = 21k
2 × 14 = 21k
k = 28/21 = 4/3
(a + b) = (6 × 4/3) = 8
c = (a + b + c) - (a + b) = (14 - 8) = 6

Number of notes of Rs. 20 = 12
Number of notes of Rs. 10 = 12/4 = 3
Number of notes of Re. 1 = 7 × 3 = 21
Total amount = 12 × 20 + 3 × 10 + 1 × 21 = 240 + 30 + 21 = Rs. 291

The age of 3^rd son = 1/3 × 60 = 20 yrs
Age of 1^st son = 20 + 8 = 28 yrs
Age of 2^nd son = 28 - 4 = 24 years
Ratio of their ages = 28 : 24 : 20 = 7 : 6 : 5
As per question, 7x + 6x + 5x = 12,00,000, i.e., 18x = 12,00,000
So, x = 66,666.66
Share of 2nd son = 6x = 6 × 66,666.66 = Rs. 4,00,000

It is known that expenditure of Brian is 2^rd/3 of his income.
Let Brian`s monthly income be $36.
Then, his expenditure will be $24.
Total savings of Brian = $12
Ratio of savings of Brian to that of Sam is given as 2 : 3.
Hence, savings of Sam = $18
Now, ratio of incomes = Brian : Sam = 3 : 4
As Brian`s income = $36, then income of Sam will be $48.
So, ratio of expenditure of Brian to that of Sam = 24 : 30 or 4 : 5