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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 58

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

Ratio Proportion

Problem

A fort has a provision for 900 men for 40 days. After 20 days, 300 men join them. For how many days more will the provision last for?

  1. 5 days
  2. 10 days
  3. 15 days
  4. 20 days
  5. 25 days

The Usual Method

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Total provision is equivalent to 900 x 40 = 36,000 man days

Of this total, 900 x 20 = 18,000 man days worth of provision is already consumed in the first 20 days by the 900 men.

Hence balance provision is equivalent to 36,000 – 18,000 = 18,000 man days.

With 300 more men joining, total number of men in the fort = 900 + 300 = 1200 men.

Let ‘x’ be the number of days for which the provision would last from the day the 300 men joined in.

Hence total number of new man days = 1200\times x = 1200x man days.

This should be equivalent to 18,000 man days.

\therefore 1200x=18000

\therefore x=\frac{18000}{1200}=15days

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Since 20 days worth of provision is already consumed, the balance provision would last for 40 – 20 = 20 more days. Since 300 more men joining there is a \frac{300}{900}\times 100=33.33% increase.

Hence to keep the total consumption constant, the number of days has to be reduced by 25%. (See concept explained in section of Percentage in Stuff to Remember)

A 25% reduction on the balance 20 days results in 20 – 5 = 15 days.

(Ans: 3)

Estimated Time to arrive at the answer = 15 seconds.
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