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[Smart Math] Ratio Proportion Problem 42

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

Problem

If the shares of A and B are in the ratio $\frac{1}{2}:\frac{1}{3}$ and also, it is equal to that of B and C. What is the proportion in which profit is divided between A, B and C?

1. 1 : 2 : 3
2. 3 : 2 : 6
3. 6 : 5 : 9
4. 2 : 3 : 4
5. 9 : 6 : 4

The Usual Method

A : B = $\frac{1}{2}:\frac{1}{3}$ = B : C

$\therefore$A : B = 3 : 2 = B : C

$\therefore$      A         :           B         :           C

3          :           2

3          :           2

9          :           6          :           4

Hence answer is 9 : 6 : 4.

(Ans: 5)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

Note that $\frac{1}{2}:\frac{1}{3}$ is the same as 0.5 : 0.33.
$\therefore$A > B > C. From amongst the options, only option ‘5’ satisfies this condition. Hence answer is 9 : 6 : 4.