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Ajit was assigned to dig a hole alone. But, after 3 hours of his work, Bipin was also assigned along with him to dig the hole. After 5 more hours, the work was complete and they were paid Rs. 660 and Rs. 330 respectively for their work. How many hours would each take to dig the hole working alone?

Ajit was assigned to dig a hole alone. But, after 3 hours of his work, Bipin was also assigned along with him to dig the hole. After 5 more hours, the work was complete and they were paid Rs. 660 and Rs. 330 respectively for their work. How many hours would each take to dig the hole working alone? Correct Answer 12 hours, 15 hours

Let Ajit and Bipin take ‘x’ and ‘y’ hours respectively to dig the hole alone

Ajit’s 1 hour work = 1/x

Bipin’s 1 hour work = 1/y

Time for which Ajit worked = 3 + 5 = 8 hours

Time for which Bipin worked = 5 hours

Work done by Ajit = 8/x

Work done by Bipin = 5/y

Now, ratio of their wages = ratio of their work done

⇒ 660 ∶ 330 = 8/x ∶ 5/y

⇒ 2 = (8/x)/(5/y)

⇒ 8/x = 10/y         ----(1)

Also, work done by Ajit and Bipin = 1

⇒ 8/x + 5/y = 1

Substituting from (1),

⇒ 10/y + 5/y = 1

⇒ 15/y = 1

⇒ y = 15

Substituting in (1),

⇒ 8/x = 10/15

⇒ x = 8 × (3/2) = 12

∴ Ajit and Bipin can dig the hole alone in 12 hours and 15 hours respectively.

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