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 1/3 B 1/4 C 1/5 D 1/7
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|
|Quantity of syrup in new mixture =||5 -||5x||litres|
|3 -||3x||+ x||=||5 -||5x|
5x + 24 = 40 - 5x
10x = 16
|So, part of the mixture replaced =||8||x||1||=||1||.|
Find the minimum integral value of n such that the division 55n/124 leaves no remainder
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.