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# [Smart Math] Ratio Proportion Problem 33

Here’s and example of a SMART MATH problem for RATIO PROPORTION. ### Problem

A can do a piece of work in 10 days, B can do the same in 30 days and C in 60 days. If A is assisted on alternate days by B and C, in how many days is the work finished?

1. 4 days
2. 5 days
3. 6 days
4. 7 days
5. 8 days

### The Usual Method

If A and B work together, $\frac{1}{10}+\frac{1}{30}=\frac{4}{30}=\frac{8}{60}$ of the work is completed.

If A and C work together, $\frac{1}{10}+\frac{1}{60}=\frac{7}{60}$ of the work is completed.

Hence if in 2 days, A & B and A & C work alternately, $\frac{8}{60}+\frac{7}{60}=\frac{15}{60}$ of the work is completed.

If $\frac{15}{60}$ of the work is completed in 2 days, to complete the whole work, it will take $\frac{60}{15}\times 2=$ 8 days.

(Ans: 4)

Estimated Time to arrive at the answer = 60 seconds.

### Using Technique

Since B and C work on alternate days with A, then in every consecutive working days, A will work for both the days and B and C for 1 day each.

Hence, A will finish $\frac{2}{10}=\frac{12}{60}$ of the work in 2 days

B will finish $\frac{1}{30}=\frac{2}{60}$ of the work in 1 day

C will finish $\frac{1}{60}$ of the work in 1 day

Thus, in 2 consecutive days, $\frac{12}{60}+\frac{2}{60}+\frac{1}{60}=\frac{15}{60}=\frac{1}{4}$ of the work is done. Hence, it will take 4 such consecutive 2 days or 8 working days to finish the work.

(Ans: 4)

Estimated Time to arrive at the answer = 15 seconds.
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