Question

X, Y and Z can complete a piece of work in 46 days, 92 days and 23 days, respectively. X started the work. Y joined him after 7 days. If Z joined them after 8 days from the beginning, then for how many days did Y work?

• A. $$12\frac{5}{7}$$
• B. $$11\frac{5}{7}$$
• C. $$10\frac{5}{7}$$
• D. $$9\frac{5}{7}$$

Answer 1

Answer:

$$11\frac{5}{7}$$

Solution:

Given data:

Days in which X can complete the work = 46 days

Days in which Y can complete the work = 92 days

Days in which Z can complete the work = 23 days

Days after which Y joined = 7 days

Days after which Z joined = 8 days

Formula used:

Efficiency = Total work / Time taken to complete work individually

Calculation:

LCM of 23, 46, 92 = 92

Assuming that the total work is 92 units.

Efficiency of x-

$\frac{92}{46}=2$units of work/day

Efficiency of y-

$\frac{92}{92}=1$

Efficiency of z-

$\frac{92}{23}=4$

Work done in 7 days by X working alone = 2 units × 7 = 14 units

Work done by X and Y on 8th day =  (2 + 1) × 1 = 3 units

Total work done until 8th day = 14 + 3 = 17 units

Remaining work = 92 - 17 = 75 units

Work done by X , Y and Z in one day = 2 + 1 + 4 = 7 units

Total time taken $=\frac{75}{7}days$

Total days worked by Y $=\frac{75}{7}+1=\frac{82}{7}=11\frac{5}{7}days$