A can do 1-2 of a work in 5 days- B can do 3-5 of the same work in 9 days and C can do 2-3 of that work in 8 days- All three of them if they work together will able to complete in 4 days-

The correct option is A True A can do the entire work in 10 days B can do the entire work in 9 × 5/3 days = 15 days C can do the entire work in 8 × 3/2 days = ...

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Byju's Answer

Standard VIII

Mathematics

Time and Work

A can do 1/2 ...

Question

A can do $\frac{1}{2}$ of a work in 5 days. B can do $\frac{3}{5}$ of the same work in 9 days and C can do $\frac{2}{3}$ of that work in 8 days. All three of them if they work together will able to complete in 4 days.

True

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False

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Solution

The correct option is A
True

A can do the entire work in 10 days
B can do the entire work in $\frac{9 \times 5}{3}$ days = 15 days
C can do the entire work in $\frac{8 \times 3}{2}$ days = 12 days

$∴ (A + B + C)^{'} s$ amount of work done in one day
$= \frac{1}{10} + \frac{1}{15} + \frac{1}{12} = \frac{6 + 4 + 5}{60} = \frac{15}{60} = \frac{1}{4}$ [LCM of 10, 15, and 12 = 60]
$∴$ They will complete the work in 4 days.

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