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Mathematics

A can do a piece of work in 24 days, A and B can do it in 16 days and A, B and C in 102310\dfrac{2}{3} days. In how many days can A and C do it working together?

Direct & Inverse Variations

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Answer

A's 1 day work = 124\dfrac{1}{24}

(A + B)'s 1 day work = 116\dfrac{1}{16}

B's 1 day work = (A + B)'s 1 day work - A's 1 day work

= 116124\dfrac{1}{16} - \dfrac{1}{24}

= (32)48\dfrac{(3 - 2)}{48}

= 148\dfrac{1}{48}

(A + B + C)'s 1 day work = 332\dfrac{3}{32}

(A + C)'s 1 day work = (A + B + C)'s 1 day work - B's 1 day work

= 332148\dfrac{3}{32} - \dfrac{1}{48}

= 9296\dfrac{9 - 2}{96}

= 796\dfrac{7}{96}

A + C can do the work in 967=1357\dfrac{96}{7} = 13\dfrac{5}{7} days

Hence, A + C can do the work in 135713\dfrac{5}{7} days.

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