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P can complete ¼ of some work in 10 days, Q can complete 40% of the same work in 48 days. R completes 1/8 of the work in 5 days and S does 1/10 of the work in 2 days. ½ of total work is done by (Q + R) and remaining work is done by (P + S). What will be the ratio of the days for completing ½ of work by (Q + R) and remaining work by the (P + S)?

P can complete ¼ of some work in 10 days, Q can complete 40% of the same work in 48 days. R completes 1/8 of the work in 5 days and S does 1/10 of the work in 2 days. ½ of total work is done by (Q + R) and remaining work is done by (P + S). What will be the ratio of the days for completing ½ of work by (Q + R) and remaining work by the (P + S)? Correct Answer 27 ∶ 12

P completes full work = 10 × 4 = 40

Q completes full work = 48 × 100/40 = 120

R completes full work = 8 × 5 = 40

S completes full work = 10 × 2 = 20

Let the total work be 120.

(∵ LCM of 40, 120, 40, & 20 is 120.)

Efficiency of P = 120/40 = 3

Efficiency of Q = 120/120 = 1

Efficiency of R = 120/40 = 3

Efficiency of s = 120/20 = 6

Days to complete ½ work by (Q + R) = 60/4 = 15

Days to complete remaining work by (P + S) = 60/9

(Q + R) ∶ (P + S)

= 15 ∶ 60/9

= 27 ∶ 12

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