# X and Y can finish a work in 15 days and 30 days respectively. Both of them worked for 5 days and left. The remaining work was completed by Z in 5 day

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X and Y can finish a work in 15 days and 30 days respectively. Both of them worked for 5 days and left. The remaining work was completed by Z in 5 days. Find total time taken to complete the work, if X and Z complete the work.
1. 7
2. 6
3. 8
4. 9

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Correct Answer - Option 2 : 6

Given:

X and Y can finish a work in 15 days and 30 days respectively. Both of them worked for 5 days and left. The remaining work was completed by Z in 5 days.

Formula:

If A and B can together finish it in t days with A and B finishing the work in a and b days respectively,

1/a + 1/b = 1/t

Calculation:

Let total work be 30 units, LCM of 15 and 30.

Efficiency X = 30/15 = 2

Efficiency Y = 30/30 = 1

Let the efficiency of Z be z

ATQ,

⇒ 5(2 + 1) + 5z = 30

⇒ 15 + 5z = 30

⇒ 5z = 15

⇒ z = 3

∴ Required time = 30/3 + 2 = 30/5 = 6 days.