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Work and Time

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$\text{A}$ alone can do a piece of work in $6$ days and $\text{B}$ alone in $8$ days. $\text{A}$ and $\text{B}$ undertook to do it for Rs. $3200.$ With the help of $\text{C},$ they completed the work in $3$ days. How much is to be paid to $\text{C}?$

  1. Rs. $375$
  2. Rs. $400$
  3. Rs. $600$
  4. Rs. $800$

2 Answers

Best answer
3 3 votes
C's 1 day's work =

1/3−(1/6+1/8)=(1/3−7/24)=1/24

A:B:C=1/6:1/8:1/24=4:3:1

C′sShare=1/8∗3200=400
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1 1 vote
Let's say the total work is to eat 24 ladoos. (Hint : take lcm of days i.e. 6,8 and 3 to make the calculation easier).
Given that A can complete the work alone in 6 days. So, A eats 4 ladoos per day.
Similarly, B eats 3 ladoos per day. So, A + B eat 7 ladoos per day.

Let's assume C eats c ladoos per day. Therefore, A + B + C eat 7 + c ladoos per day.
And they take 3 days to finish 24 ladoos.

Therefore, (3)(7+c) = 24. This gives c = 1.
So, out of 24 ladoos :
A eats total 4*3 = 12 ladoos
B eats total 3*3 =  9 ladoos
C eats total 1*3 =  3 ladoos

And the ratio comes out as 4 : 3 : 1 (A : B : C)
So, the amount C receives will be [1/(4+3+1)]*3200
which comes out to be (1/8)*3200 = 400
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