[Smart Math] Ratio Proportion Problem 59

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

Problem

R can do a piece of work in 20 days and K in 25 days. They work together for 5 days and then K leaves. In how many days would R finish the work?

1. 5
2. 9
3. 10
4. 11
5. 12

The Usual Method

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R can finish of the work in 1 day.

K can finish of the work in 1 day.

Thus total work finished by R and K working together for 5 days = .

Hence remaining work = .

Since R has to work alone now and R can finish of the work in 1 day, so for R to finish of the work, it will take,

1                     

x

By cross multiplication, we get:

11 days more.

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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R will finish or 25% of the work in 5 days. K will finish or 20% of the work in 5 days. So, work remaining to be done = 100% – (25% + 20%) = 55%.

Since R takes 5 days to finish 25% of the work, he will take 10 days to finish 50% of the work. So for 55%, R will take a little over 10 days, so 11 days to finish. (Also, 55% is a multiple of 11, so the answer should also be a multiple of 11.)

(Ans: 4)

Estimated Time to arrive at the answer = 10 seconds.
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