\(12m*20=18w*16=24c*18\)

\(5m=6w=9c\)

We need to find the efficiency of \(m,w,c\). We have many ways to approach this like taking \(LCM(5,6,9)=90\). \(m=\frac{90}{5}=18\). Similarly, \(w=15\) and \(c=10\)

Another approach would be; \(5m=6w => \frac{m}{w}=\frac{6}{5}\) and \(6w=9c => \frac{w}{c}=\frac{3}{2}\)

\(\frac{m}{w}=\frac{6*3}{5*3}=\frac{18}{15}\) or \(\frac{w}{c}=\frac{3*5}{2*5}=\frac{15}{10}\)

Find the \(total \ work = 12*18*20 = 4320\)

Work done by \((8w+16c)*9 = (8*15+16*10)*9=(120+160)*9 = 2520\)

Remaining work \(= 4320 - 2520=1800\)

Completed by 10m, so efficiency of \(10m = 10*18 = 180\)

No of days required \(= \frac{1800}{180 }=10\) days

Ans C

Solution:


We see that the rate of the 12 men is 1/20 per day. Thus, the rate of each man is (1/20) / 12 = 1/240 per day. Similarly, the rate of the 18 women is 1/16 per day, and so the rate of each woman is (1/16) / 18 = 1/288 per day. The rate of 24 children is 1/18 per day, and the rate of each child is (1/18) / 24 = 1/432 per day. Therefore, the portion of work done by 8 women and 16 children in 9 days is (8 x 1/288 + 16 x 1/432) x 9 = (1/36 + 1/27) x 9 = 1/4 + 1/3 = 7/12. Therefore, the remaining 5/12 of the work can be done by 10 men in (5/12) / (10 x 1/240) = (5/12)/(1/24) = 5/12 x 24 = 10 days.

Answer: C
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I'm confused how total work has been calculated 12 x 18 x 20
Can someone guide for this part

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SantoshSukumaran

Substitute the value of \(m\) or \(w\) or \(c\) at any of the below equation to calculate the total work;
\(12m∗20=18w∗16=24c∗18 \)
It is always equal in all cases. Hope this clarifies your query.
Cheers meanup!