rishi worked on a set of mathematics problems for 20 min and finished 4/15 of it . he then called raja .working together they finished the compelete set in 22 minutes.how long would rishi and raja have taken to finish the set individually.
Answers
In 20m Rishi can complete 4/15.
So in x min he can complete 15/15(full homework)
x = time taken by rishi to complete whole work alone.
so, 20 - 4/15
x - 15/15 or 1.
20/4/15 = x
x =75 min.
So, rishi can finish whole work in 75min.
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Rate of work of rishi is 1/75.
(means he can finish 1/75 of work in 1min)
Now if he call Raja they could finish the remaining work in 22min.
work remaining =15/15 - 4/15 =11/15.
in 22 min -- 11/15 work
in y min -- 15/15 work.
so y = 22×1÷11/15
= 30 min.
so together they can finish whole in 30m.
rate of work of them combined = 1/30.
rate of work of rishi + rate of work of raja = combined rate of work.
1/75 +1/rate of raja =1/30
1/rate of raja = 1/30 - 1/75.
1/rate of raja = 3/150=1/50
1/raja = 1/50 .
raja = 50
so raja will take 50 min to finish the work alone.