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40 men can complete a work in 48 days. 64 men started and did the same work for xx days. After xx days, 32 men increased, so, the remaining work is completed in 162316\frac{2}{3} days, then the value of xx is

Solution

✅ Correct Option: 1

Given: 4040 men can complete the work in 4848 days

Total work =40×48=1920= 40 \times 48 = 1920 man-days

Think of it as 19201920 identical tasks that need to be done.


6464 men worked for xx days

Work completed =64×x=64x= 64 \times x = 64x man-days


After xx days, 3232 more men join the team

New total workforce =64+32=96= 64 + 32 = 96 men

These 9696 men complete the remaining work in 162316\frac{2}{3} days

Converting the mixed number: 1623=50316\frac{2}{3} = \frac{50}{3} days


Work completed by 9696 men in 503\frac{50}{3} days:

=96×503= 96 \times \frac{50}{3}

=48003=1600= \frac{4800}{3} = 1600 man-days


Total work == Work done in first xx days ++ Work done in final phase

1920=64x+16001920 = 64x + 1600

64x=1920−160064x = 1920 - 1600

64x=32064x = 320

x=32064=5x = \frac{320}{64} = 5


Therefore, x=5x = 5 days

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