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# [Smart Math] Ratio Proportion Problem 48

Here’s and example of a SMART MATH problem for 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

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

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.
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