Arafat and Asif were each paid X taka in advanced to do a certain job together. Arafat worked on the job for 10 hours and Asif worked 2 hours less than Arafat. If Asif gave Arafat Y taka of his payment so that they would have received the same hourly wage, what was the amount in taka, in terms of Y, that Arafat was paid in advance?

Question: Arafat and Asif were each paid X taka in advanced to do a certain job together. Arafat worked on the job for 10 hours and Asif worked 2 hours less than Arafat. If Asif gave Arafat Y taka of his payment so that they would have received the same hourly wage, what was the amount in taka, in terms of Y, that Arafat was paid in advance?

Solution:
Given,
Arafat worked 10 hours,
∴ Asif worked (10 - 2) = 8 hours

Given that,
Each was paid X taka in advance.
Asif gives Y taka to Arafat.

Now,
Arafat's net payment = X + Y
Asif's net payment = X - Y

According to the question,
(X + Y)/10 = (X - Y)/8.
⇒ 8(X + Y) = 10(X - Y)
⇒ 8X + 8Y = 10X - 10Y.
⇒ 8Y + 10Y = 10X - 8X
⇒ 18Y = 2X
⇒ X = (18/2) × Y
⇒ X = 9Y
Thus Arafat was paid 9Y taka in advance.