Question

Two numbers are in the ratio 3:5. If
12 is added to both the numbers, then
the ratio becomes 5:7. The sum of the
given two numbers is
(1) 32
(2) 40
(3) 48
(4) 56​

Answer 1

❒ Let the two numbers are 3x and 5x respectively.

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${\boldsymbol{According\: to \:the\: Question :}}$

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• If 12 is added to both the numbers, then the ratio becomes 5:7.

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Therefore,

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$\begin{gathered}:\implies\sf \dfrac{3x + 12}{5x + 12} = \dfrac{5}{7} \\\\\\:\implies\sf 5(5x + 12) = 7(3x + 12) \\\\\\:\implies\sf 25x + 60 = 21x + 84\\\\\\:\implies\sf 25x - 21x = 84 - 60\\\\\\:\implies\sf 4x = 24\\\\\\:\implies\sf x = \cancel\dfrac{24}{4}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 6}}}}}\;\bigstar\end{gathered}$

❒ Hence, the numbers are,

• First number, 3x = 3(6) = 18
• Second number, 5x = 5(6) = 30

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$\therefore{\underline{\sf{Hence, \; two \; numbers\; are\; \bf{18 \; and \; 30}.}}}$

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Now,

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• Sum of the given two numbers is,

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18 + 30 = 48.

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$\therefore{\underline{\sf{Hence, \: sum \; of \; the \; two \; numbers \; is \; \bf{Option\; 3) \; 48 }.}}}$