$16$ men can complete a work in $12$ days, $24$ children can complete the same work in $18$ days, $12$ men and $8$ children started working and after $8$ days, $3$ more children joined them. How many days will they now take to complete the remaining work ?
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$2$ days
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$4$ days
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$6$ days
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$8$ days
B
Correct answer
Explanation
16 men = 12 days, so 1 man = 192 days. 24 children = 18 days, so 1 child = 432 days. Daily work of 1 man = 1/192, 1 child = 1/432. 12 men + 8 children = 12/192 + 8/432 = 1/16 + 1/54 = 35/432. In 8 days, they do 8 * 35/432 = 35/54. Remaining work = 19/54. New force = 12 men + 11 children = 12/192 + 11/432 = 1/16 + 11/432 = 38/432 = 19/216. Days = (19/54) / (19/216) = 4 days.