What number must be added to each term of the ratio $14 : 23$ so that it may becomes equal to $8 : 11$ ?

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Solution

Calculation of the required number:
Consider that $x$ is added to each of the terms in the ratio $14 : 23$ . Now, as per the given information, the ratio is as follows.
$\Rightarrow 14 + x : 23 + x = 8 : 11 \Rightarrow \frac{14 + x}{23 + x} = \frac{8}{11} \Rightarrow 11 (14 + x) = 8 (23 + x) (C r o s s m u l t i p l y b o t h s i d e s) \Rightarrow 154 + 11 x = 184 + 8 x \Rightarrow 11 x - 8 x = 184 - 154 (S e p a r a t i n g t h e v a r i a b l e a n d c o n s \tan t t e r m s) \Rightarrow 3 x = 30 \Rightarrow x = \frac{30}{3} (D i v i d i n g b o t h s i d e s b y 3) ∴ x = 10$
Final Answer: 10 is added to each term of the ratio $14 : 23$ to make it $8 : 11$ .

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