Important Questions Test: Ratio & Proportion- 3 - CAT MCQ

► Assume that Y produces 4P units in unit time.
► Then X and Z produce P and 2P units in the same time.
► So, Total shoes produced = 7P, Fraction of the total number of shoes produced by machine Z = 2/7

Tax = Fixed + Variable

► Since Mr Kalyan pays Rs 6200 and Mrs Kalyan pays Rs 7700, so it can be inferred that for Rs 10,000 (Difference between their salaries), one has to pay Rs 1500 as the variable tax.
► So, Fixed component of tax = Rs 5200. The point worth to be noted here is the fact that tax is to be paid over an above Rs 50,000.
► So, the variable tax percentage above Rs 50,000 = 10%. Now the answer can be calculated using options.

► Assume the distance = 9 units.
► So, the ratio of the time taken = 9:3:1
So, the answer = (9/1):(3/3):(1/9)
⇒ 81:9:1

T = 2π * (√l/g)

T increases by 10%, new time period 0.1T

(1T + 0.1T) = 2π * (√l/g)

1.1T = 2π * (√l/g)

i.e 21% increase in the length of the pendulum.

► Let the common factor be k.
► Hence, the number of articles of type P, Q and R will be 3k, 2k and 3k respectively
► Also, Unit price of article x Number of articles = Total amount for the articles
∴ 300 x 3k + 180 x 2k + 120 x 3k = 6480
⇒ k = 4
∴ Number of articles of Type Q = 2k = 8

► Whatever is the total number of boys, it should be divisibie by 8, 6, 12 
► For total number of girls should be divisible by 12, 15 and 4, Now use options.

► Whatever is the total number of boys, it should be divisibie by 8, 6 and 12 
► For total number of girls should be divisible by 12, 15 and 4, Now use options.

It is given that in drum 1, A and B are in the ratio 18 : 7.

Let us assume that in drum 2, A and B are in the ratio x : 1.

It is given that drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7.

By equating concentration of A

Therefore, we can say that in drum 2, A and B are in the ratio 239/161 : 1 or 239 : 161.

Let the score of Amal and Bimal be 11k and 14k
Let the scores be increased by x
So, after increment, Amal’s score =  11k + x and Bimal’s score = 14k + x
According to the question, 
On solving, we get x = 42/9 k
Ratio of Bimal’s new score to his original score

Hence, option A is the correct answer.

Let the number of marbles with Raju and Lalitha initially be 4x and 9x.
Let the number of marbles that Lalitha gave to Raju be a.

It has been given that (4x+a)/(9x-a) = 5/6
24x + 6a = 45x – 5a
11a = 21x
a/x = 21/11

Fraction of original marbles given to Raju by Lalitha = a/9x (Since Lalitha had 9x marbles initially).
a/9x = 21/99
= 7/33.

Therefore, option D is the right answer.

The proportion of water in the first mixture is 1/3
The proportion of Liquid A in the first mixture is 2/3
The proportion of water in the second mixture is 1/4
The proportion of Liquid B in the second mixture is 3/4
The proportion of water in the third mixture is 1/5
The proportion of Liquid C in the third mixture is 4/5
As they are mixed in the ratio 4:3:2, the final amount of water is

The final amount of Liquid A in the mixture is 4 x 2/3 = 8/3
The final amount of Liquid B in the mixture is 3 x 3/4 = 9/4
The final amount of Liquid C in the mixture is 2 x 4/5 = 8/5
Hence, the ratio of Water : A : B : C in the final mixture is

From the given choices, only option C  is correct.

a : b = 3:4 and b : c = 2:1 => a:b:c = 3:4:2

=> a = 3x, b = 4x , c = 2x
=> a + b + c = 9x

=> a + b + c is a multiple of 9.
From the given options only, option C is a multiple of 9

The ratio of L, S, J for popcorn = 7 : 17 : 16
Let them be 7x, 17x, and 16x
The ratio of L, S, J for chips = 6 : 15 : 14
Let them 6y, 15y and 14y
Given, 40x = 35y, x = 7y/8
Jumbo popcor = 16x = 16 * 7y/8 = 14y
Hence, the ratio of jumbo popcorn and jumbo chips = 1 : 1