Question

. The ratio of monthly income of two persons A and B is 8: 7 and their monthly expenditure ratio is 19:16. If both individuals have a
monthly savings of ૨ 1250, find
everyone's monthly income.​

Answer 1

A n s w e r

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G i v e n

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• The ratio of monthly income of two persons A and B is 8: 7

• Their monthly expenditure ratio is 19:16

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F i n d

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• Their monthly income

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S o l u t i o n

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Given that , The ratio of monthly income of two persons A and B is 8: 7

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Thus ,

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• Let the monthly income of A be 8i

• Let the monthly income of B be 7i

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Also given that , Their monthly expenditure ratio is 19:16

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Thus ,

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• Let the expenditure of A be 19e

• Let the expenditure of B be 16e

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$\underline{ \underline{\bold{\texttt{Savings :}}}}$

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➠ Income - Expenditure = Savings ⚊⚊⚊⚊ ⓵

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$\underline{ \underline{\bold{\texttt{For A :}}}}$

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We assumed income to be 8i , expenditure to be 19e and given that A saves 1250 per months

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• Income = 8i

• Expenditure = 19e

• Savings = 1250

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: ➜ 8i - 19e = 1250 ⚊⚊⚊⚊ ⓵

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⟮ Multiplying equation ⓵ by 7 ⟯

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: ➜ 7(8i - 19e) = 1250 × 7

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: ➜ 56i - 133e = 8750 ⚊⚊⚊⚊ ⓶

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$\underline{ \underline{\bold{\texttt{For B :}}}}$

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We assumed income to be 7i , expenditure to be 16e and given that B saves 1250 per months

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• Income = 7i

• Expenditure = 16e

• Savings = 1250

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: ➜ 7i - 16e = 1250 ⚊⚊⚊⚊ ⓷

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⟮ Multiplying equation ⓷ by 8 ⟯

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: ➜ 8(7i - 16e) = 1250 × 8

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: ➜ 56i - 128e = 10000 ⚊⚊⚊⚊ ⓸

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⟮ Equation ⓸ - ⓶ ⟯

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: ➜ 56i - 128e -(56i - 133e) = 10000 - 8750

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: ➜ 56i - 128e - 56i + 133e = 1250

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: ➜ 5e = 1250

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: ➜ $\sf e = \dfrac { 1250 } { 5 }$

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: ➜ e = 250 ⚊⚊⚊⚊ ⓹

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⟮ Putting e = 250 from ⓹ to ⓷ ⟯

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: ➜ 7i - 16e = 1250

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: ➜ 7i - 16(250) = 1250

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: ➜ 7i - 4000 = 1250

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: ➜ 7i = 1250 + 4000

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: ➜ 7i = 5250

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: ➜ $\sf i = \dfrac { 5250 } { 7 }$

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: ➜ i = 750

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$\underline{ \underline{\bold{\texttt{Income of A :}}}}$

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➠ 8i

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• i = 750

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: ➜ 8(750)

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: : ➨ 6000

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• Hence the income of A is Rs 6000

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$\underline{ \underline{\bold{\texttt{Income of B :}}}}$

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➠ 7i

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• i = 750

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: ➜ 7(750)

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: : ➨ 5250

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• Hence the income of B is Rs 5250

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∴ The incomes of A & B are Rs 6000 & 5250 respectively