Practice Test: Ratio & Proportion- 2 - CAT MCQ

∴ Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38000.

Let x be the number of new men joined the garrison,
The total quantity of food is = 3600(20) (1.5) kg ----------1
Now the available food will be consumed by (3600 + x) men
(3600 + x) (12) (2) kg  --------------2
1 = 2
Solving both the equations
3600(20) (1.5) = (3600 + x) (12) (2)
108000 = 86400 + 24x
21600 = 24x
X = 900
900 more men joined the garrison.

Considering the three kinds of tea are A, B, and C.

The price of kind A = Rs 800 per kg.

The price of kind B = Rs 500 per kg.

The price of kind C = Rs 300 per kg.

They were mixed in the ratio of 2 : 3: 5.

1/6 of the total mixture is sold for Rs 700 per kg.

Assuming the ratio of mixture to A = 12kg, B = 18kg, C =30 kg.

The total cost price is 800 * 12 + 500 * 18 + 300 * 30 = Rs 27600.

Selling 1/6 which is 10kg for Rs 700/kg the revenue earned is Rs 7000.

In order to have an overall profit of 50 percent on Rs 27600.

Thes selling price of the 60 kg is Rs 27600 * 1.5 = Rs 41400.

Hence he must sell the remaining 50 kg mixture for Rs 41400 – Rs 7000 = 34400.

Hence the price per kg is Rs 34400/50 = Rs 688

Initially let’s consider A and B as one component

The volume of the mixture is doubled by adding A(60% alcohol) i.e they are mixed in 1:1 ratio and the resultant mixture has 72% alcohol.

Let the percentage of alcohol in component 1 be ‘x’.

Using allegations , 

Percenage of alcohol in A = 60% ⇒ Let’s percentage of alcohol in B = x%

The resultant mixture has 84% alcohol. ratio = 1:3

Using allegations, 

⇒ x= 92%

Let the volume of Metals A,B,C we 3x, 4x, 7x

Ratio weights of given volume be 5y,2y,6y

∴ 15xy + 8xy + 42xy = 130 ⇒ 65xy = 130 ⇒ xy = 2.

∴ `The weight, in kg. of the metal C is 42xy = 84.

Assuming the investment of Amala, Bina, and Gouri be 300x, 400x and 500x, hence the interest incomes will be

300x × 6/100 = 18x, 400x × 5/100 = 20x and 500x × 4/100 = 20x

Given, Bina’s interest income exceeds Amala by 20x - 18x = 2x = 250  ⇒ x = 125

Now, total interest income = 18x + 20x + 20x = 58x = 58 × 125 = 7250

Let the scores of Rama, Anjali and Mohan be r, a, m.

It is given that Rama’s score was one-twelfth of the sum of the scores of Mohan and Anjali

The scores of Rama, Anjali and Mohan after review = r + 6, a + 6, m + 6

a + 6 : m + 6 : r + 6 = 11 : 10 : 3

Let a + 6 = 11x ⇒ a= 11x - 6

m + 6 = 10x ⇒ m = 10x - 6

r + 6 = 3x ⇒ r = 3x - 6
Substituting these values in equation (1), we get

12(3x - 6) = 21x - 12

x = 4

Anjali’s score exceeds Rama’s score by (a - r) = 8x = 32