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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 13

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

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

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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

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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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