Question

The ratio of two numbers is 3:5. If 12 is added to both the numbers, then the ratio formed is 5:7. The sum of given two numbers is *​

Answer 1

Answer:

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

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

AccordingtotheQuestion:

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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}

:⟹

5x+12

3x+12

=

7

5

:⟹5(5x+12)=7(3x+12)

:⟹25x+60=21x+84

:⟹25x−21x=84−60

:⟹4x=24

:⟹x=

4

24

:⟹

x=6

★

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❒ 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}.}}}∴

Hence,twonumbersare18and30.

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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\; c) \; 48 }.}}}∴

Hence,sumofthetwonumbersisOptionc)48.