Question

20. Find the number which when added to each term of the ratio 27 : 35, changes the ratio to 4:5​

Answer 1

★ SOLUTION

$the \: given \: ratio \: is \: \: \frac{27}{35} \:$

Now, let x be added to the given ratio.

$now \: new \: ratio \: = \frac{27 + x}{35 + x}$

According to question,

$\implies \: \: \frac{27 + x}{35 + x} = \frac{4}{5} \\ \\ \implies \: \: 5 \: (27 + x) \: = 4 \: (35 + x) \\ \\ \implies \: \: 135 + 5x = 140 + 4x \\ \\ \implies \: \: 5x - 4x = 140 - 135 \\ \\ \implies \: \: x = 5$

Hence, the required number is 5.

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