Question

Two numbers are in the ratio 5:7. If they differ by 42, find the greater number?​

Answer 1

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★Question :

➊ Two numbers are in the ratio 5:7 . If they differ by 42 , find the greatest number?

✯ To find:

➡ Greatest number =?

✮ Solution :

➜ Let x and y be the required two numbers where y > x.

$\\ \therefore \sf \: the \: ratio \: \frac{x}{y} = \frac{5}{7} \implies \: \boxed { \sf{x = \frac{5y}{7} }} \to \: (1)$

• And the difference is 42

$\\ \implies \sf \: y - x = 12 \: \: ...equation \: (2)$

$\\ \implies \sf \: y - \frac{5y}{7} = 12 \: \to \: using \: equation(1)$

$\\ \implies \sf \: 7y - 5y = 12 \times 7$

$\implies \sf \: 2y = 84 \:$

$\\ \implies \sf \: \boxed{ \sf\: y = 42} \:$

From equation (2) we get,

$\\ \implies \sf \: 42 - x = 12$

$\\ \implies \sf \: 42 - x - 12 = 0$

$\implies \sf \boxed{\sf \: x = 30}$

Hence the larger number is 42

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