Question

the sum of two number is 26 and their difference is 14.if three times the larger number is divided by the smallest number then the quotient​

Answer 1

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

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

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• The sum of two number is 26

• The difference between them is 14

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

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• If three times the larger number is divided by the smaller number then the quotient

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

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• Let the 1st number be "a"

• Let the 2nd number be "b"

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

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Given that the sum of two number is 26

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➜ a + b = 26 ⚊⚊⚊⚊ ⓵

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Also given that the difference between them is 14

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➜ a - b = 14 ⚊⚊⚊⚊ ⓶

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⟮ Adding equation ⓵ & ⓶ ⟯

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➜ a + b + a - b = 26 + 14

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➜ 2a = 40

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➜ $\sf a = \dfrac { 40 } { 2 }$

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➠ a = 20 ⚊⚊⚊⚊ ⓷

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• Hence the 1st number is 20

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⟮ Putting a = 20 from ⓷ to ⓵ ⟯

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➜ a + b = 26

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➜ 20 + b = 26

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➜ b = 26 - 20

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➠ b = 6

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• Hence the second number is 6

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Clearly the 1st number is greater then the 2nd number

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$\underline{\bold{\texttt{3 times the greater number :}}}$

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➜ 3(a)

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➜ 3(20)

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➜ 60

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$\underline{\bold{\texttt{3 times the greater number divided by the smaller one :}}}$

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• 3 times greater = 60

• Smaller number = 6

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➜ $\sf \dfrac { 60 } { 6 }$

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➨ 10

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• Hence when 3 times the greater number is divided by the smaller one the quotient is 10