12 men take 6 days to complete a piece of work. They worked for a period of 2 days. After that, they were joined by 4 more men. How many more days will be taken by them to complete the remaining work?

Solution

12 men = 6 days Work done by 12 men in one day = 1/6 Work done by 12 men in 2 days = 1/6 × 2 = 1/3 Remaining work = 1 - 1/3 = 2/3 Now, 4 men joined them Therefore, 2/3 rd of work is done by 16 men in x days We have the formula, M1 × D1 / W1 = M2 × D2 / W2 Here, M1 = 12, D1 = 2 and W1 = 1/3 M2 = 16, D2 = x and W2 = 2/3 (12 × 2)/(1/3) = (16 × x )/(2/3 ) x = 3 days ALTERNATE SHORTCUT METHOD M1 × D1 = M2 × D2 12× 6 = 12× 2 +(12+4) × x 72 = 24 +16 x 48 = 16 x So x=3days