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# [Smart Math] Ratio Proportion Problem 3

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

### Problem

In an alloy of three metals A, B and C, the quantity of metal A is 4/5th of B and that of B is 3/4th of C. What is the quantity in lb of each metal in 47 lbs of the alloy? (In the order of A, B and C.)

1. 13, 22, 12
2. 12, 13, 22
3. 12, 15, 20
4. 20, 15, 12
5. 10, 20, 18

### The Usual Method

A = 4/5 B                                            B = 3/4 C

$\therefore$ 5A = 4B                                              4B = 3C

$\therefore$ A : B = 4 : 5                                        B : C = 3 : 4

$\therefore$
A         :           B         :           C

4          :           5
aaaaaaaaaa 3         :           4

12        :           15        :           20

Also, 12 + 15 + 20 = 47 lbs

Hence, A = 12 lbs, B = 15 lbs and C = 20 lbs.

(Ans: 3)

Estimated Time to arrive at the answer = 60 seconds.

### Using Technique

The first step is to eliminate those options whose sum $\ne$ 47. Thus option ‘5’ is eliminated as sum of 10 + 20 + 18 = 48.
For option ‘2’, 5 x 12 $\ne$ 4 x 13, hence ‘2’ is also eliminated. Thus answer is option ‘3’.