Categories
Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 48

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

Ratio Proportion

Problem

The income of Jack and Jill are in the ratio of 2 : 3 and their expenses are 3 : 5. If both save $2000, what is Jill’s income?

  1. $15000
  2. $12000
  3. $10000
  4. $8000
  5. $6000

The Usual Method

[contentblock id=google-adsense-post]

Income of Jack = 2x

\therefore Income of Jill = 3x

Also expense of Jack = 3y

And expense of Jill = 5y

\therefore 2x-3y=2000=3x-5y

\therefore 2x-3y=3x-5y

\therefore 2y=x

Substituting this in the, we get:

3\left( 2y \right)-5y=2000

\therefore y=2000

\therefore x=2\times 2000=4000

\therefore Income of Jill = 3 x 4000 = $12000

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

[contentblock id=google-adsense-post]

Jill’s income is 3x, hence it is a multiple of 3.

This eliminates options ‘3’ and ‘4’.

Now, after removing the savings from the income, we get expenses. Expenses for Jill is 5y.

Hence, 15000 – 2000 = 13000 (13 is not a multiple of 5)

12000 – 2000 = 10000 (10 is a multiple of 5)

6000 – 2000 = 4000 (4 is not a multiple of 5)

Hence option ‘2’.

(Note: All numbers are taken in their ‘000s as 2000 is in ‘000).

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds.
[starrater tpl=10]

[contentblock id=smartmath-blockquote]

Leave a Reply

Your email address will not be published. Required fields are marked *