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# [Smart Math] Arithmetic Problem 21

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

### Problem

Find the sum of reciprocal of two numbers whose sum is 12 and product is 32.

1. $\frac{5}{3}$
2. $\frac{8}{3}$
3. 3
4. $\frac{3}{8}$
5. 8

### The Usual Method

Let one of the numbers be ‘x’.

Hence the other number is (12 – x)

Also $\left( 12-x \right)\times x=32$

$\therefore 12x-x^{2}=32$

$\therefore x^{2}-12x+32=0$

$\therefore \left( x-8 \right)\times \left( x-4 \right)$

$\therefore x=8$ and $x=4$

Hence one of the numbers is 4 and the other number is 8.

Hence sum of reciprocals = $\frac{1}{4}+\frac{1}{8}=\frac{3}{8}$

(Ans: 4)

Estimated Time to arrive at the answer = 30 seconds.