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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 59

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

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 \frac{1}{20} of the work in 1 day.

K can finish \frac{1}{25} of the work in 1 day.

Thus total work finished by R and K working together for 5 days = \frac{5}{20}+\frac{5}{25}=\frac{25+20}{100}=\frac{45}{100}.

Hence remaining work = 1-\frac{45}{100}=\frac{55}{100}.

Since R has to work alone now and R can finish \frac{1}{20} of the work in 1 day, so for R to finish \frac{55}{100} of the work, it will take,

1                      \frac{1}{20}

x \frac{55}{100}

By cross multiplication, we get:

\frac{55}{100}\times \frac{20}{1}= 11 days more.

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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R will finish \frac{5}{20} or 25% of the work in 5 days. K will finish \frac{5}{25} 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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