Two men A and B working together complete a piece of work which it would have taken them 30 and 40 days respectively to complete if they worked separately. If they received a payment of Rs. 2100, B’s share is:a)Rs. 900b)Rs. 800c)Rs. 1200d)Rs. 1300e)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Two men A and B working together complete a piece of work which it would have taken them 30 and 40 days respectively to complete if they worked separately. If they received a payment of Rs. 2100, B&rsquo;s share is:a)Rs. 900b)Rs. 800c)Rs. 1200d)Rs. 1300e)None of theseCorrect answer is option 'A'. Can you explain this answer?

Answer

Received a payment of Rs. 600 more than A. How much money did B receive?

Let's assume that A's daily work rate is x units per day and B's daily work rate is y units per day.

If A works alone, he would complete the work in 30 days, so the total work is 30x units.
If B works alone, he would complete the work in 40 days, so the total work is 40y units.

When A and B work together, their combined work rate is (x+y) units per day. The total work is completed in 30 days, so the total work is (30(x+y)) units.

Since the total work is the same in both cases, we can set up the equation:
30x = 40y

Now we know that B received a payment of Rs. 600 more than A, so B received (A + 600) Rs.
The total payment received is Rs. 2100, so A received (2100 - (A + 600)) = (1500 - A) Rs.

Now we can set up another equation based on the work done and the payment received:
30(x+y) = 2100
30(x+y) = 30x + 30y = 2100

Substituting the equation 30x = 40y into 30x + 30y = 2100, we get:
40y + 30y = 2100
70y = 2100
y = 2100/70 = 30

Substituting y = 30 into 30x = 40y, we get:
30x = 40*30
30x = 1200
x = 1200/30 = 40

So A's daily work rate is x = 40 units per day and B's daily work rate is y = 30 units per day.

Now we can calculate how much money B received:
B received (A + 600) = (40 + 600) = 640 Rs. Answer: \boxed{640}.

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