Solve the following riddle by finding the unknown number :

$" A t h i r d o f m e t i m e s h a l f o f m e i s a s i x t h m o r e t h a n f o u r . F i n d m y d i v i s i o n a n d m u l t i p l i c a t i o n e q u a t i o n s t o k n o w a b o u t m e m o r e "$

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Solution

The correct option is A 5
$Let us take the unknown number as A$

$Forming a mathematical equation step by step from the riddle, we get:$

$A t h i r d o f m e = A \div 3 = \frac{A}{3}$

$H a l f o f m e = A \div 2 = \frac{A}{2}$

$S i x t h m o r e t h a n f o u r = 4 + \frac{1}{6} = 4 \frac{1}{6} = \frac{(6 \times 4) + 1}{6} = \frac{25}{6}$

$∴ The line " A t h i r d o f m e t i m e s h a l f o f m e i s a s i x t h m o r e t h a n f o u r " can be expressed as:$

$\frac{A}{3} \times \frac{A}{2} = \frac{25}{6}$

$⟹ \frac{A \times A}{3 \times 2} = \frac{25}{6}$

$⟹ A \times A = 25$

$But, 5 \times 5 = 25$

$∴ A = 5$

$Hence, the m u l t i p l i c a t i o n e q u a t i o n can be written as:$

$\frac{5}{3} \times \frac{5}{2} = \frac{25}{6}$

$The corresponding d i v i s i o n e q u a t i o n will be:$

$\frac{25}{6} \div \frac{5}{2} = \frac{5}{3} O R \frac{25}{6} \div \frac{5}{3} = \frac{5}{2}$

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