Question

A and B together can do a piece

of work in 19 days. A is thrice as

efficient as B. If A and B together

works for 7 days, then in how many

days the remaining work will be

completed by B alone?​

Answer 1

Answer:

A finishes 10 days before B, so time taken for A, TaTa , is time taken by B, TbTb less 10 days :

Ta=Tb−10Ta=Tb−10

A is 3 times as efficient as B, and so time taken for A, TaTa is 1313 of TbTb :

3Ta=Tb3Ta=Tb

Ta=3Ta−10Ta=3Ta−10

2Ta=102Ta=10

∴Ta=5∴Ta=5

∴Tb=3T∴Tb=3T a=15a=15

A does 1515 or 315315 of the job each day.

B does 115115 of the job each day.

A & B do 315+115=415315+115=415 each day.

3×415=12153×415=1215

4×415=16154×415=1615

So they’ll finish on Day 4.