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P can complete 15\frac{1}{5}51​ of a work in 12 days and Q can complete 16\frac{1}{6}61​ of a work in 8 days. In how many days can both P and Q togeth
Question

P can complete 15\frac{1}{5} of a work in 12 days and Q can complete 16\frac{1}{6} of a work in 8 days. In how many days can both P and Q together complete the work?

A.

2623\frac{2}{3}​​

B.

2423\frac{2}{3}​​

C.

2545\frac{4}{5}​​

D.

2245\frac{4}{5}​​

Correct option is A

P can complete 15\frac{1}{5}​ of a work in 12 days.

Total Work done by P in = 12 × 5 = 60 days

Q can complete 16\frac{1}{6}​ of a work in 8 days.

Total Work done by Q in = 8 × 6 = 48days

Total Work = LCM of 60 and 48 = 240 unit

Efficiency of P and Q are 24060=4 unit per day and 24048=5 unit per day\frac {240}{60} = 4 \,unit \,per \,day \,and\, \frac{240}{48 } = 5 \,unit\, per\, day​​

Total time taken by both of them = 2404+5=\frac{240}{4+5 }=​ 2623\frac{2}{3}

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