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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 21

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

Ratio Proportion

Problem

The ratio of the number of ladies to gents at a party was 1 : 2, but when 2 ladies and 2 gents leave, the ratio became 1 : 3. How many people were at the party originally?

  1. 35
  2. 40
  3. 18
  4. 15
  5. 12

The Usual Method

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Let the original number of ladies in the party be ‘x’.

Hence, the number of gents = 2x

Thus, \frac{x-2}{2x-2}=\frac{1}{3}

\therefore 3x-5=2x-2

\therefore x=4

Hence, number of gents in the party = 2x = 8

Hence, total number of people in the party = 4 + 8 = 12.

(Ans: 5)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Since, the original ratio of ladies to gents = 1 : 2, the total number of guests = 1x + 2x = 3x.

Also, the new ratio of ladies to gents = 1 : 3, the total number of guests = 1y + 3y = 4y

Hence the total number of guests should be a multiple of both 3 and should become a multiple of 4 after 4 is subtracted from it. This means that the original number of guest should be a multiple of 3 as well as 4 or a multiple of 12. The only option satisfying this condition is option ‘5’.

(Ans: 5)

Estimated Time to arrive at the answer = 10 seconds.
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