Practice Test: Ratio & Proportion- 2 - UPSC MCQ

Originally, let the number of boys and girls in the college be 7x and 8x respectively.

Their increased number is (120% of 7x) and (110% of 8x).

⇒ (120/100 × 7x) and (110/100 × 8x)

⇒ (42x/5) and (44x/5)

∴ The required ratio = (42x/5) : (44x/5) = 21 : 22

Ratio of salaries of Ravi and Sumit = 2 : 3.
Increased salary = 4000 each.
New ratio of Ravi and Sumit = 40 : 57.

Calculation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.

Then, (2x + 4000)/(3x + 4000) = 40/57

⇒ 57(2x + 4000) = 40(3x + 4000)
⇒ 6x = 68000
⇒ 3x = 34000

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

Let A = 2k, B = 3k, and C = 5k.
A's new salary = (115/100) of 2k = (115/100 × 2k) = (23k/10)
B's new salary = (110/100) of 3k = (110/100 × 3k) = (33k/10)
C's new salary = (120/100) of 5k = (120/100 × 5k) = 6k
∴ New ratio = (23k/10) : (33k/10) : 6k = 23 : 33 : 60

Let 40% of A = (2/3) B.

Then, (40A/100) = (2B/3).

⇒ (2A/5) = (2B/3).

⇒ A/B = ((2/3) × (5/2)) = 5/3.

∴ A : B = 5 : 3.

Let the fourth proportional to 5, 8, 15 be x.

Then, 5 : 8 = 15 : x

⇒ 5x = (8 × 15)

x = (8 × 15) / 5 = 24.

Let the number of 25 p, 10 p, and 5 p coins be x, 2x, and 3x respectively.
Then, the sum of their values = Rs.
(25x/100 + 10 × 2x/100 + 5 × 3x/100) = 60x/100
∴ 60x/100 = 30
x = (30 × 100) / 60 = 50
Hence, the number of 5 p coins = (3 × 50) = 150.

Let the numbers be 3x and 5x.

Then, (3x - 9) / (5x - 9) = 12 / 23

⇒ 23(3x - 9) = 12(5x - 9)

⇒ 9x = 99

⇒ x = 11

∴ The smaller number = (3 × 11) = 33.

(x × 5) = (0.75 × 8) ⇒ x = (6/5) = 1.20

Let the three parts be A, B, C. Then,

A : B = 2 : 3 and B : C = 5 : 8 = (5 × 3/5) : (8 × 3/5) = 3 : 24/5

⇒ A : B : C = 2 : 3 : 24/5 = 10 : 15 : 24

⇒ B = (98 × 15/49) = 30.

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.