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# [Smart Math] Ratio Proportion Problem 10

Here’s and example of a SMART MATH problem for 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

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

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’.