Arithmetic

Time & Work

Medium

X, Y and Z together can do a piece of work in 16 (4/11) days. X and Y together can do the same work in 20 days. In how many days will Z alone finish the 60% of the work?

59 days

54 days

53 days

51 days

✅ Correct Option: 2

X, Y and Z together finish work in 16 (4/11) days.

Converting to improper fraction:

$16 \dfrac{4}{11} = \dfrac{16 \times 11 + 4}{11}$

$= \dfrac{176 + 4}{11}$

$= \dfrac{180}{11}$ days

Work rate of (X + Y + Z) together:

Work rate $= \dfrac{1}{\text{time taken}} = \dfrac{1}{180/11} = \dfrac{11}{180}$ work per day

X and Y together take 20 days.

Work rate of (X + Y) together:

Work rate $= \dfrac{1}{20}$ work per day

Z's work rate alone is the difference between the combined rate and (X + Y)'s rate:

Z's work rate $= \dfrac{11}{180} - \dfrac{1}{20}$

$= \dfrac{11}{180} - \dfrac{9}{180}$

$= \dfrac{2}{180}$

$= \dfrac{1}{90}$ work per day

Z completes the full work in:

Time $= \dfrac{1}{1/90} = 90$ days

For 60% of the work:

Time $= 90 \times 0.6$

$= 54$ days

Therefore, Z alone will finish 60% of the work in 54 days.

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Solution

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