Question Detail

If a:b = 2:3 and b:c = 4:3, then find a:b:c

8:12:9
2:3:8
2:3:9
2:3:12

Answer: Option A

Explanation:

$\begin{aligned} a:b = 2:3 \\ b:c = 4:3 = (4*\frac{3}{4} : 3*\frac{3}{4}) \\ = 3:\frac{9}{4} \\ a:b:c = 2:3:\frac{9}{4} \\ = 8:12:9 \end{aligned}$

1. The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and that of the second to the third is 5:8, then the second number is

Answer: Option D

Explanation:

$\begin{aligned} a:b = 2:3 \\ b:c = 5:8 = (5*\frac{3}{5} : 8*\frac{3}{5}) \\ = 3:\frac{24}{5} \\ a:b:c = 2:3:\frac{24}{5} \\ = 10:15:24 \\ b = 98*\frac{15}{49} \\ = 30 \end{aligned}$

2. If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be

Answer: Option B

Explanation:

Let the numbers be 3x, 2x and 5x.
Then,
9x + 4x + 25x =1862
⇒ 38x = 1862
⇒ x = 49 ⇒ x = 7.
middle number = 2x = 14

3. Find the fourth proportion to 2,3,6

Answer: Option C

Explanation:

2:3 :: 6:x

=> 2/3 = 6/x
=> x = 18/2
=> x = 9

4. If Rs. 782 is divided into three parts, proportional to
$\begin{aligned} \frac{1}{2}:\frac{2}{3}:\frac{3}{4} \end{aligned}$

find the first part.

Answer: Option B

Explanation:

$\begin{aligned} \frac{1}{2}:\frac{2}{3}:\frac{3}{4} \\ = 6:8:9\\ \text{First part =} 782 * \frac{6}{23} \\ = 204 \end{aligned}$

5. In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is

20 liters
30 liters
50 liters
60 liters

Answer: Option D

Explanation:

Quantity of Milk = 60*(2/3) = 40 liters
Quantity of water = 60-40 = 20 liters

As per question we need to add water to get quantity 2:1

=> 40/(20+x) = 1/2
=> 20 + x = 80
=> x = 60 liters