24 men can complete a work in 16 days. 32 women can complete the same work in 24 days. 16 men and 16 women started working and worked for 12 days. How many more men are to be added to complete the remaining work in 2 days?
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24 men ----------- 16 days ------------ 1 complete work
1 man ------------ 1 day ------------1/(24*16) portion work
32 women ----------- 24 days ------------ 1 complete work
1 woman ------------ 1 day ------------1/(32*24) portion work
Hence,
1 man &1 woman ------------ 1 day ------------{1/(32*24) + 1/(24*16)} portion work = 1(/24)*(1/16 + 1/32) = (1/24)*(3/32) = (1/8)*(1/32)
Now,
16 man & 16 woman ------------ 1 day ------------ 16* (1/8)*(1/32) portion work = 2*(1/32) = 1/16
16 man & 16 woman ------------ 12 day ------------ 12*(1/16) = 3/4
Remaining work - 1/4
Now, extra work in next 2 days: 1/4 - 2*(1/16) = 1/8
Then, extra men required in next 2 days: (24*16)/(2*8) = 24 .
1 man ------------ 1 day ------------1/(24*16) portion work
32 women ----------- 24 days ------------ 1 complete work
1 woman ------------ 1 day ------------1/(32*24) portion work
Hence,
1 man &1 woman ------------ 1 day ------------{1/(32*24) + 1/(24*16)} portion work = 1(/24)*(1/16 + 1/32) = (1/24)*(3/32) = (1/8)*(1/32)
Now,
16 man & 16 woman ------------ 1 day ------------ 16* (1/8)*(1/32) portion work = 2*(1/32) = 1/16
16 man & 16 woman ------------ 12 day ------------ 12*(1/16) = 3/4
Remaining work - 1/4
Now, extra work in next 2 days: 1/4 - 2*(1/16) = 1/8
Then, extra men required in next 2 days: (24*16)/(2*8) = 24 .
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