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Question

A takes 6 days less than the time taken by B to finish a piece of work. If both AandB together can finish it in 4 days, How many days will B take to finish the work?


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Solution

Step 1. Assuming that B alone takes x days to finish the work.

Therefore A alone can finish the work in (x-6) days

Step 2. Now ,

A's one day’s work + B's one day’s work =1x+1(x-6)

Step 3. According to question ,

both AandB together can finish it in 4 days

Therefore work done by AandB together in one day=14

we have,

1x+1(x-6)=14x-6+xx(x-6)=142x-6x2-6x=144(2x-6)=x2-6x8x-24=x2-6xx2-6x-8x+24=0x2-14x+24=0x-(12+2)x+24=0x-12x-2x+24=0x(x-12)-2(x-12)=0(x-12)(x-2)=0either(x-2)=0or(x-12)=0x=2orx=12

Step 4. As x can not be less than 6.

So, we have x=12

Hence, B will take 12 days to finish the work.


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