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

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

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❒ Hence, the numbers are,

• First number, 3x = 3(6) = 18

• Second number, 5x = 5(6) = 30

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

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

Answer 2

Answer:

Given :-

Two number are in ratio 3:5. When 12 added the ratio become 5:7.

To Find :-

Sum

Solution :-

Let the number be 3y and 5y.

$\sf \pink { \dfrac{3y + 12}{5y + 12} = \dfrac{5}{7}}$

$\sf \blue{5(5y + 12) = 7(3y + 12)}$

$\sf \pink{25y + 60 = 21y + 84}$

$\sf \red{25y - 21y = 84 - 60}$

$\sf \orange{4y = 24}$

$\sf \green{y = \dfrac{24}{4}}$

$\frak \red{y = 6}$

Numbers are :-

$\sf \gray {3(6) = 18}$

$\sf \purple {5(6) = 30}$

Sum = 30 + 18 = 48