Question

A solution contain wine and water in ratio 2:1 Out of it 36 litre solution is replaced by 15 litre water. Again 52 litre solution is replaced by same quality of water. Now wine water ratio become 8:7 Find difference between water quantity in initial and final solution.​

Answer 1

Answer:

Let's say

wine=2A litre

water=A litre

Total solution=2A+A=3A litre

36 litre water is replaced by 15 litre of water

Wine =2A-(2/3)36=2A-24 litre

Water=A-(1/3)36

A-12+15=A+3 litre

Wine=2(A-12)

Water=A+3

Total=3A-21=3(A-7)

now 26 litre solution is replaced by water

wine=2(A-12)-26×2(A-12)/3(A-7)

=(6A^2-114A+504-52A+624)/3(A-7)

Water=A+3-26(A+3)/3(A-7)+26

=(3A^2+66A-609-26A-78)/3(A-7)

=(6A^2-116A+1128)/3A^2+46A-687)

=8/7

(3A^2-83A+564)/(3A^2+40A-687)

=4/7

=21A^2-581A+3948=12A^2+160A-2748

=9A^2-741A+6696=0

=3A^2-247A+2232=0

=3A^2-216A-31A+2232=0

=3A(A-72)-31(A+72)=0

=(3A-31) (A-72)=0

=A=31/3 OR A=72

=A=72

Water in initial=72

Water in final=A+3-26(A+3)/3(A-7)+26

A=72=91

Water in final=91

Difference btw water quantity in initial and final solution =91-72=19