Correct Answer: 13 and 27

Explanation:

Total no.of boys : no. of girls = 13:27

       27             :                13

Correct Answer: 2:3

Explanation:

By the rule of alligation:
Cost of 1 kg rice of 1st kind                  Cost of 1 kg rice of 2nd kind 

 

 

  Required ratio = 60 : 90 = 2 : 3

Correct Answer: 5:3

Explanation:

W 1 : A 1 W 2 : A 2 . . . . . W N : A N

  2 : 3                   4 : 5                    5 : 7 

 

W 1 W 1 + A 1 = 2 5 W 2 W 2 + A 2 = 4 9 W N W N + A N = 5 12

= 72/180

= 80/180

= 75/180  

                     

 

 =>     5   :   3

 

Therefore, the ratio is  5: 3

Correct Answer: 5 litres

Explanation:

Total quantity of mixture = 75 litre

Milk  :  Water  =  4  :  1   

            

                   3       :       1

Correct Answer: 15

Explanation:

Let quantity of mixture be x liters.

 

Suppose a container contains x units of liquid from which y units are taken out and replaced by Water. After operations , the quantity of pure liquid =  x 1 - y x n units, Where n = no of operations . 

 

So, Quantity of Milk =  x 1 - 6 x 2  

 

Given that, Milk : Water = 9 : 16 

 

=> Milk : (Milk + Water) = 9 : (9+16)

 

=> Milk : Mixture = 9 : 25 

 

 Therefore,  x 1 - 6 x 2 x = 9 25

 

=> x = 15 liters

Correct Answer: 22 lit

Explanation:

Let the capacity of the pot be 'P' litres.
Quantity of milk in the mixture before adding milk = 4/9 (P - 8)
After adding milk, quantity of milk in the mixture = 6/11 P.
6P/11 - 8 = 4/9(P - 8)
10P = 792 - 352 => P = 44.

The capacity of the pot is 44 liters.

Correct Answer: 15 boys and 35 girls

Explanation:

Average money received by each = 118/50 = Rs. 2.36
Therefore, Ratio of No.of boys and girls = 56 : 24 = 7 : 3
Therefore, Number of boys = 50 x (7/10) = 35
Number of girls = 50 - 35 = 15

Correct Answer: 91 liters

Explanation:

         Milk             Water 

         74%             26%        (initially) 

         76%             24%        ( after replacement) 

 

  Left amount = Initial amount  1 - r e p l a c e d a m o u n t t o t a l a m o u n t 

   24  = 26 1 - 7 k

=> k = 91 

Correct Answer: 80 lit

Explanation:

From the given data,

let the initial quantity of the mixture = 5x

Then,

$$\begin{gathered} 2 x - 16 3 x - 24 + 40 = 1 4 \\ 8 x - 64 = 3 x + 16 \\ 5 x = 80 \\ x = 16 lit \end{gathered}$$

 

Then the initial quantity of the mixture = 5x = 5 x 16 = 80 lit.

Correct Answer: 120 liters

Explanation:

W i n e ( l e f t ) W a t e r ( a d d e d ) = 343 169

 

It means    W i n e ( l e f t ) W i n e ( i n i t i a l a m o u n t ) = 343 512   ? 343 + 169 = 512

 

Thus ,       

343 x = 512 x 1 - 15 K 3

 

  ? 343 512 = 7 8 3 = 1 - 15 k 3

 

=> K = 120

Thus the initial amount of wine was 120 liters.