Question

A bucket contains a mixture of two liquids P and Q in the ratio 11:7. If 9 liters of the mixture is replaced by 9 liters of liquid Q, then the ratio of the two liquids become 5:9.How much of the liquid Q does the buckets have , in liters

Answer 1

Answer:

Statement of the given problem,

A bucket contains a mixture of two liquids A and B in the proportion 7:5. If 9 L of the mixture is replaced by 9 L of liquid B, then the ratio of the two liquids becomes 7:9. How much of the liquid A was there in the bucket?

Let (A1, B1) & (A2, B2) denote (liquid A, liquid B) in initial & final mixtures respectively.

Hence from above data we get following relations,

A1 : B1 = 7 : 5 …… (1a) [initial mixture]

A2 : B2 = 7 : 9 …… (2a) [final mixture]

From (1a) we get,

A1 = 7/(7 + 5)*(A1 + B1)

or A1 = (7/12)*(A1 + B1) …… (1b)

B1 = 5/(7 + 5)*(A1 + B1)

or B1 = (5/12)*(A1 + B1) …… (1c)

When 9 L of the initial mixture is replaced by 9 L of liquid B then we get,

A2 = A1 - (7/12)*9

or A2 = (7/12)*(A1 + B1) - (7/12)*9 [from (1b)]

or A2 = (7/12)*(A1 + B1 - 9) …… (2b)

B2 = B1 - (5/12)*9 + 9

or B2 = (5/12)*(A1 + B1) - (5/12)*9 + 9 [from (1c)]

or B2 = (5/12)*(A1 + B1) + (7/12)*9 …… (2c)

From (2a), (2b) & (2c) we get,

[(7/12)*(A1 + B1 - 9)] : [(5/12)*(A1 + B1) + (7/12)*9] = 7 : 9

or 9*(7/12)*(A1 + B1 - 9) = 7*[(5/12)*(A1 + B1) + (7/12)*9]

or (A1 + B1)(63 - 35)/12 = (81 + 63)*7/12

or A1 + B1 = 144*7/28 = 36

Hence from (1b) & (1c) we get,

A1 = (7/12)*(A1 + B1) = (7/12)*36 = 21 (L)

B1 = (5/12)*(A1 + B1) = (5/12)*36 = 15 (L)

Therefore it is evident from above that

the amount of liquid A in the initial mixture was 21 L [Ans]