Question : X and Y together can do a work in 10 days. Y and Z together can do the same work in 15 days. Z and X together can do the same work in 12 days. In how many days can Z alone do the same work?
Option 1: 80 days
Option 2: 60 days
Option 3: 40 days
Option 4: 50 days
Correct Answer: 40 days
Solution :
Given,
X and Y together can do a work in 10 days.
Y and Z together can do the same work in 15 days.
Z and X together can do the same work in 12 days.
Let the total work = LCM (10, 15, 12) = 60
⇒ Efficiency of X + Y = $\frac{60}{10}$ = 6 units/day
⇒ Efficiency of Y + Z = $\frac{60}{15}$ = 5 units/day
⇒ Efficiency of Z + X = $\frac{60}{12}$ = 4 units/day
⇒ Efficiency of 2(X + Y + Z) = 15 units/day
$\therefore$ Efficiency of (X + Y + Z) = 7.5 units/day
Now, Efficiency of Z = 7.5 – 6 = 1.5 units/day
$\therefore$ Z alone can do the work = $\frac{60}{1.5}$ = 40 days
Hence, the correct answer is 40 days.
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