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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 3

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

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

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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

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The first step is to eliminate those options whose sum \ne 47. Thus option ‘5’ is eliminated as sum of 10 + 20 + 18 = 48.

The next step is to identify the metal with maximum or minimum quantity. Because A = 4/5 B and B = 3/4 C; the metal C is of maximum quantity and A is of minimum quantity. Thus options ‘1’ and ‘4’ are eliminated. This leaves us with options ‘2’ and ‘3’ only. Since, A = 4/5 B; 5A = 4B.

For option ‘2’, 5 x 12 \ne 4 x 13, hence ‘2’ is also eliminated. Thus answer is option ‘3’.

(Ans: 3)

Estimated Time to arrive at the answer = 15 seconds.
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