In a vessel, there are two types of liquids A and B in the ratio of `4:7`. 33 lit of the mixture is taken out and 2 lit of type B liquid is poured into it, the new ratio (A:B) thus formed is `2:3`. Find the initial quantity of mixture in the vessel ?

Options

A. 32 lit
B. 21 lit
C. 10 lit
D. 11 lit

Answer

D

Explanation

Let the initial quantity of mixture in vessel be x lit
ATQ,
`(x xx (4)/(11)-2)/(x xx (7)/(11)-21+2)=(2)/(3)`
`rArr (4x-132)/(7x-209)=(2)/(3)`
`rArr 12x-396=14x-418`
`rArr 2x=22 " " rArr x=11 lit`