## A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup

Option:

A 1/3 B 1/4 C 1/5 D 1/7

Solution:

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.

 Quantity of water in new mixture = 3 - 3x + x litres 8

 Quantity of syrup in new mixture = 5 - 5x litres 8

 3 - 3x + x = 5 - 5x 8 8

5x + 24 = 40 - 5x

10x = 16

 x = 8 . 5

 So, part of the mixture replaced = 8 x 1 = 1 . 5 8 5

11th April 2019

79

## Find the minimum integral value of n such that the division 55n/124 leaves no remainder

Find the minimum integral value of n such that the division 55n/124 leaves no remainder

1. 124
2. 123
3. 31
4. 62

As 55 does not have factor common to 124, so for 55n to be exactly divisible by 124, n should be a multiple of 124.

Hence the minimum value that n can have is 124 it self

The correct option is A.

29th March 2019

125