Question

I can finish a work in 15 days at 8 hrs a
day. You can finish it in 62/3 days at 9 hrs
a day. Find how many days we can finish
it working together 10 hrs a day.
​

Answer 1

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• In 7.2 days(approx) we can finish it together if we work for 10 hrs a day.

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Given :

• I can finish the work in 15 days if I work 8hrs a day.
• You can finish the same work in 62/3 days if you work 9 hrs a day.

To Find :

• In how many days we can finish
• it working together 10 hrs a day = ?

Solution :

Total time taken by me to complete the work :

$\implies$ 15 × 8

$\implies$ 120 hrs

Total time taken by you to complete the work :

$\implies$ 62/3 × 9

$\implies$ 186 hrs

Together we can complete the work per hour :

$:\implies \sf \: \: \: \dfrac{1}{120} + \dfrac{1}{186} \\ \\ \\ \\ :\implies \sf \: \: \: \dfrac{186 + 120}{120 \times 186} \\ \\ \\ \\ :\implies \sf \: \: \: \dfrac{306}{ \: 22320 \: } \\ \\ \\ \\ :\implies \sf \: \: \: \dfrac{1}{72}(approx)$

• It will take 72 hrs to complete the total work.

Working 10hrs each day, it would take :

$\implies$ 72/10

$\implies$ 7.2 days

Therefore, in 7.2 days(approx) we can finish it together if we work for 10 hrs a day.

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