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# [Smart Math] Arithmetic Problem 8

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

### Problem

C’s age is 1.5 times the averages age of A, B and C. A’s age is half the average age of the three. What was their average age two years ago if the present age of B is 10 years?

1. 10 years
2. 8 years
3. 14 years
4. 7 years
5. 5 years

### The Usual Method

Let the present average age of the three be ‘x’ years.

C’s present age = 1.5x years

A’s present age = 0.5x years

B’s present age = 10 years

$\therefore$ Average age = $\frac{1.5x+0.5x+10}{3}=x$

$\therefore$x = 10 years

$\therefore$C’s present age = 1.5 x 10 = 15 years

$\therefore$A’s present age = 0.5 x 10 = 5 years

$\therefore$C’s age two years ago = 15 – 2 = 13 years

$\therefore$A’s age two years ago = 5 – 2 = 3 years

$\therefore$B’s age two years ago = 10 – 2 = 8 years

$\therefore$ Average age two years ago = $\frac{13+3+8}{3}=8$years

(Ans: 2)

Estimated Time to arrive at the answer = 75 seconds.

### Using Technique

Since, $\frac{1.5x+0.5x}{2}=x$