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# [Smart Math] Algebra Problem 27

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

### Problem

If the sum of money is divided among ‘n’ children, each child will receive $60. If another child is added to the group and the amount is distributed again each child will receive$50. What is the sum of money to be distributed?

1. $3 2.$30
3. $300 4.$3000
5. Cannot be determined

### The Usual Method

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Let $‘x’ be the sum of money, than $60\times n=x$ Also when a child joins, $50\times (n+1)=x$ $\therefore 60n=50(n+1)$ $\therefore 60n=50n+50$ $\therefore 10n=50$ $\therefore n=5$ Hence, $x=60\times n=60\times 5=$$300

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

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Since $60\times n=x$ and also $50\times (n+1)=x$; x should be a multiple of both 50 and 60. Hence simply find the LCM of 60 and 50 which is 300 which is the answer.

(Ans: 3)

Estimated Time to arrive at the answer = 10 seconds.
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## One reply on “[Smart Math] Algebra Problem 27”

PhantomMathematiciansays:

That’s smart. It should be clicking in the minds of the people preparing for competitive exams in no time at all. Because it’s logical. Plain, simple, but smart.