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P can complete a work in 12 days and Q can complete a work in 24 days. P leaves the work on 6th day and rest work is done by Q. If both were to be paid Rs 3000 collectively for the whole work then what is the wage of Q?1. Rs 15002. Rs 20003. Rs 21004. Rs 24005. Rs 1800 |
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Answer» Correct Answer - Option 1 : Rs 1500 Given: P = 12 Days Q = 24 days Formula used: 1/T = (1/T1) + (1/T2) Here, T1 = work done in days by 1, T2 = work done in days by 2 Calculation: P completes work in 12 days and Q in 24 days ⇒ 1/T = (1/12) + (1/24) ⇒ 1/T = (2 + 1)/24 ⇒ Together they complete work in 8 days Work done for 6 days ⇒ Left work = 1 - (6/8) ⇒ Left work = 1/4 ⇒ Q completes work in 24 days hence; left work would be completed in (1/4 × 24) ⇒ Left work would be completed in 6 days Now, Total work done is LCM of 12 and 24 = 24 units ⇒ Efficiency of P = 2 units/day ⇒ Efficiency of Q = 1 unit/day ⇒ P’s work in units = 6 × 2 ⇒ Q’s work in units = 12 × 1 ⇒ Total work done = 12 + 12 ⇒ Total work done = 24 units ⇒ 24 units = Rs 3000 Hence, 12 units = 3000/2 ∴ Wage of Q is Rs 1500 |
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