Question

Shivam alone can do a work in 12 days and Maanik alone can do it in, 15 days. Both started the work together and after working for 4 days, Shivam left the work. After 2 more days, Veer joins Maanik and the whole work is completed in 2 days more than the time taken by Shivam and Maanik together to do that work. Find the time taken by Veer alone to do that work?​

Answer 1

Solution :-

→ LCM of 12 & 15 = 60 unit = Let Total work.

So,

→ Efficiency of Shivam = (Total work) / (Total No. of Days.) = (60/12) = 5 units/day.

Similarly,

→ Efficiency of Maanik = (Total work) / (Total No. of Days.) = (60/15) = 4 units/day.

then,

→ Efficiency of shivam and Maanik = 5 + 4 = 9 units/day.

therefore,

→ Time taken by Shivam and Maanik together to do that work = (Total work) / (Efficiency of both) = 60/9 = (20/3) days. ------- Eqn.(1)

now, given that, both together work for 4 days.

so,

→ in 4 days the completed = Efficiency of both * 4 = 9 * 4 = 36 units of work.

and, for next two days Maanik work alone.

so,

→ in 2 days Maanik alone completed = 2 * Efficiency of Maanik = 2 * 4 = 8 units of work .

then,

→ Left work now = 60 - (36 + 8) = 16 units.

Now, given that, Veer joins Maanik and the whole work is completed in 2 days more than the time taken by Shivam and Maanik together to do that work.

Let us assume that, (Veer + Maanik) works for x days and completed the work .

A/q,

from Eqn.(1) , we get,

→ 4 days(Shivam and Maanik) + 2 days(Maanik) + x(Veer + Maanik) = Total Days by (Shivam and Maanik) + 2 days .

→ 6 + x = (20/3) + 2

→ x = (20/3) + 2 - 6

→ x = (20/3) - 4

→ x = (20 - 12)/3

→ x = (8/3) Days.

hence,

→ Days * Efficiency of (Veer + Maanik) = Left work

→ (8/3)[Veer + 4] = 16

→ 8(Veer + 4) = 16 * 3

→ Veer + 4 = 6

→ Veer = 6 - 4

→ Veer = 2 units / day.

∴

→ Time taken by Veer alone to do that work = (Total work) / (Efficiency) = 60 / 2 = 30 days. (Ans.)

Veer alone can complete the same work in 30 days.

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