Question

two numbers are in a ratio of 3:5 If 7 is added to each of them then the ratio is 11:16 Find the numbers
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Answer 1

Given that, two numbers are in the Ratio of 3:5.

⠀⠀ ☯ Let's consider that the number be 3x and 5x.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀

$\sf\underline{\bigstar\; According \ to \ Question \ Now\;:}$⠀

• If each number is increased by 7, the ratio becomes 11 : 16.

⠀⠀⠀

Therefore,

⠀⠀

$:\implies\sf \dfrac{3x + 7}{5x + 7} = \dfrac{11}{16} \\\\\\:\implies\sf 16(3x + 7) = 11(5x + 7) \\\\\\:\implies\sf 48x + 112 = 55x + 77 \\\\\\:\implies\sf 55x - 48x = 112 - 77 \\\\\\:\implies\sf 7x = 35 \\\\\\:\implies\sf x = \cancel\dfrac{35}{7} \\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 5}}}}}$

Hence,

⠀⠀

• First Number, 3(5) = 15
• Second Number, 5(5) = 25

⠀⠀⠀⠀

$\therefore\:{\underline{\sf{The \ required \ Numbers \ are \ {\textsf{\textbf{15 and 25.}}}.}}}$⠀⠀⠀

Answer 2

Numbers are $\mathfrak \red {15 \: and \: 25}$

Given :-

• Two numbers are in ratio 3:5
• If 7 added to each then the ratio become 11:16

To Find :-

Numbers

Solution :-

Let the number be 3x and 5x

Now,

When increased by 7

3x + 7/5x + 7 = 11/16

16(3x + 7) = 11(5x +7)

48x + 112 = 55x + 77

55x - 48x = 112 - 77

7x = 35

x = 35/7

x = 5