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X alone can do a piece of work in 6 days and Y alone in 8 days. X and Y undertook the work for ₹ 48000. With the help of Z, they completed the work in 3 days. How much is Z’s share?

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#### Solution

X can do the work in 6 days.

X’s 1 day work = `1/6`

X’s share for 1 day = `1/6 xx 48000` = ₹ 8000

X’s share for 3 days = 3 × 8000 = ₹ 24000

Y can complete the work in 8 days.

Y’s 1 day work = `1/8`

Y’s 1 day share = `1/8 xx 48000` = ₹ 6000

Y’s 3 days share = ₹ 6000 × 3 = ₹ 18000

(X + Y)’s 3 days share = ₹ 24000 + ₹ 18000 = ₹ 42000

Remaining money is Z’s share

∴ Z’s share = ₹ 48000 – ₹ 42000 = ₹ 6000

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