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# [Smart Math] Algebra Problem 18

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

### Problem

Tom is 6 years elder to Dick. 20 years ago, Tom was 15 times older than Harry, but now Dick is twice as old as Harry. What is the age of Dick?

1. 44
2. 48
3. 50
4. 52
5. 54

### The Usual Method

Let the present age of Dick be ‘x’ years.

Hence, age of Harry = $\frac{x}{2}$ years.

Age of Harry 20 years ago = $\frac{x}{2}-20$

Present age of Tom = $x+6$

Age of Tom 20 years ago = $x+6-20=x-14$

$\therefore \left( x-40 \right)15=2\left( x-14 \right)$

$\therefore 15x-600=2x-28$

$\therefore 13x=572$

$\therefore x=\frac{572}{13}=44$years

(Ans: 1)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

Assume each option to be the right answer and reverse calculate to check as follows:

Option Age of Dick Age of Tom Age of Tom 20 years back

a.                     44                    50                    30                    (multiple of 15)

b.                     48                    54                    34                    (not a multiple of 15)

c.                     50                    56                    36                    (not a multiple of 15)

d.                     52                    58                    38                    (not a multiple of 15)

e.                     54                    60                    40                    (not a multiple of 15)

(Note: If you go sequentially taking one option at a time and start with option ‘1’, you do not have to go further as option ‘1’ will give the age of Tom 20 years back as a multiple of 15. No other option leads to a multiple of 15.)

(Ans: 1)

Estimated Time to arrive at the answer = 30 seconds.

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