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# [Smart Math] Ratio Proportion Problem 13

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

### Problem

What is A’s share of an amount of \$7000, if he gets $\frac{1}{2}$ of what B and $\frac{1}{4}$ of what C gets?

1. 700
2. 900
3. 1000
4. 1100
5. 1200

### The Usual Method

Let the share of A be ‘x

Hence, B’s share = 2x and C’s share = 4x.

Hence total amount shared = $x+2x+4x=7000$

$\therefore 7x=7000$

$\therefore x=\frac{7000}{7}=1000$

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

Assuming option ‘1’ to be the answer,

A’s share = 700

B’s share = 1400 and

C’s share = 2800

But, 700 + 1400 + 2800 $\ne$ 7000 and hence options ‘1’ is not the answer.

Assuming option ‘2’ to be the answer,

A’s share = 900

B’s share = 1800 and

C’s share = 3600

But, 900 + 1800 + 3600 $\ne$ 7000 and hence options ‘2’ is not the answer.

Assuming option ‘3’ to be the answer,

A’s share = 1000

B’s share = 2000 and

C’s share = 4000

But, 1000 + 2000 + 4000 = 7000 and hence options ‘3’ is the answer.

No need to check further as there can be only one single answer.

(Ans: 3)

Estimated Time to arrive at the answer = 30 seconds, but much easier.
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