Question

Two vessels P and Q were partially filled with milk.

80% of the contents of P were transferred to Q. 60%

of the contents of Q were then transferred back to P.

At this stage, the ratio of the quantities of milk in

P and Q is 23 : 12. Find the ratio of the initial

volumes of milk is P and Q.

(A) 5 : 3 (B) 10 : 6

(C) 15 : 11 (D) 5 : 2​

Answer 1

${\huge{\red{\underline{5:2}}}}$

Step by Step:

"P and Q were partially filled with milk"

P and Q contain p units and q units of milk, respectively.

"80% of the contents of P were transferred to Q"

0.8p units are transferred from P to Q.

Now P contains 0.20p and Q contains 0.80p+q.

"60% of the contents of Q were then transferred back to P"

0.6(0.80p+q) units are transferred from Q to P.

Now P contains 0.20p+0.6(0.80p+q) = 0.68p + 0.6q

and Q contains 0.4(0.80p+q) = 0.32p + 0.4q

"At this stage ,the ratio of the quantities of milk in P and Q is 23:12"

(0.68p + 0.6q):(0.32p + 0.4q) = 23:12

12(0.68p + 0.6q) = 23(0.32p + 0.4q)

8.16p + 7.2q = 7.36p + 9.2q

0.8p = 2q

p/q = 2/0.8 = 5/2

p:q = 5:2

${{\red{\underline{Please \: \: Mark \: \: as \: \: \: Brainliest}}}} \\ \small\fbox\orange{I'm requesting you with my folded hands!!}$