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 D

Explanation:

From question, lets assume that two numbers are 3x and 5x.

\begin{aligned}
\text{then, }\frac{3x - 9}{ 5x - 9} = \frac{12}{23}\\
=> \text{23(3x - 9) = 12(5x - 9)}\\
=> 9x = 99 \\
=> x = 11
\end{aligned}
So numbers are 3(11) = 33, 5(11) = 55.
Smaller number is 33.

Answer: Option B

Explanation:

Let the boy are 8x and Girls are 5x

=> 5x = 200
=> x = 40

Total students = 8x+5x = 13x = 13(40) = 520

Answer: Option C

Explanation:

Treat 2:9 as 2/9 and x:18 as x/18, treat :: as =

So we get 2/9 = x/18
=> 9x = 36
=> x = 4

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

Answer: Option B

Explanation:

Dog : Hare = (3*3) leaps of hare : 5 leaps of hare
= 9 : 5