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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 10

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

Ratio Proportion

Problem

In a game, A’s score was 2/7th of the total and B’s was 2/7th of the remainder. If A scored 32 runs more than B, what was the total score?

  1. 350
  2. 364
  3. 378
  4. 392
  5. 420

The Usual Method

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Let the total score = x

Hence, A’s score = \frac{2x}{7}

\therefore Remainder = 1-\frac{2}{7}=\frac{5}{7}

\therefore B’s score = \frac{2}{7}\times \frac{5x}{7}=\frac{10x}{49}

Also, since A scored 32 runs more than B,

\frac{2x}{7}-32=\frac{10x}{49}

\therefore \frac{14x}{49}-32=\frac{10x}{49}

\therefore 4x=32\times 49

\therefore x=8\times 49=392

(Ans: 4)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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If x is the total score, than A’s score = \frac{2x}{7} and B’s score = \frac{10x}{49}. Since B’s score is a fractional multiple of x, with denominator = 49, the value of x, should be a multiple of 49 as B’s score has to be an integer. The only option that is a multiple of 49 from the options is option ‘4’.

(Ans: 4)

Estimated Time to arrive at the answer =15 seconds.

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