Question

Two numbers are in ratio 7 : 11. If 7 is added to each number the ratio becomes 2 : 3, find the numbers:

1 point​

Answer 1

Answer:

Given

′

2

′

no's are in the ratio 7:11

′

7

′

is added to these no's then the ratio 2:3

Let 1st no= 7x

2nd no= 11x

11x+7

7x+7

=

3

2

3(7x+7)=2(11x+7)

21x+21=22x+14

22x−21x=21−14

x=7

1st no =7×7=49

2nd no =11×7=77

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• Two numbers are in ratio 7 : 11

• If 7 is added to each number the ratio becomes 2 : 3

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• The two numbers

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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Given that , the two numbers are in ratio 7 : 11

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• Let the first number be 7a

• Let the second number be 11a

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$\underline{\bold{\texttt{First number :}}}$

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➠ 7a ⚊⚊⚊⚊ ⓵

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$\underline{\bold{\texttt{Second number :}}}$

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➠ 11a ⚊⚊⚊⚊ ⓶

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$\underline{\bold{\texttt{7 is added to First number :}}}$

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➜ 7a + 7 ⚊⚊⚊⚊ ⓷

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$\underline{\bold{\texttt{7 is added to Second number :}}}$

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➜ 11a + 7 ⚊⚊⚊⚊ ⓸

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$\rm{ \large{\pink{\underline\blue{According \: to \: the \ question :}}}}$

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If 7 is added to each number the ratio becomes 2 : 3

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Thus ,

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From ⓷ & ⓸

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➜ $\sf \dfrac { 7a + 7 } { 11a + 7 } = \dfrac { 2 } { 3 }$

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➜ 3(7a + 7) = 2(11a + 7)

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➜ 21a + 21 = 22a + 14

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➜ 22a - 21a = 21 - 14

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➜ a = 7 ⚊⚊⚊⚊ ⓹

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⟮ Putting a = 7 from ⓹ to ⓵ ⟯

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➜ 7a

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➜ 7(7)

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➨ 49

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• Hence the first number is 49

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⟮ Putting a = 7 from ⓹ to ⓶ ⟯

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➜ 11a

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➜ 11(7)

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➨ 77

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• Hence the second number is 77

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∴ The numbers are 49 and 77