Ratio, Proportion
- The income of A and B are in the ratio 2 : 3 and their expenditures are in the ratio 1 : 2. If each saves ₹ 24,000, find A’s income.
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Let the income of A and B be ₹ 2x and ₹ 3x. and their expenditures be ₹ y and ₹ 2y respectively.
∴ 2x – y = 24000 ...(i)
and 3x – 2y = 24000 ...(ii)
By equation (i) × 2 – (ii),
4x – 2y – 3x + 2y = 24000
⇒ x = 24000
∴ A’s income = 2 × 24000
= ₹ 48000Correct Option: D
Let the income of A and B be ₹ 2x and ₹ 3x. and their expenditures be ₹ y and ₹ 2y respectively.
∴ 2x – y = 24000 ...(i)
and 3x – 2y = 24000 ...(ii)
By equation (i) × 2 – (ii),
4x – 2y – 3x + 2y = 24000
⇒ x = 24000
∴ A’s income = 2 × 24000
= ₹ 48000
- The ratio of the incomes of A and B as well as of B and C is 3 : 2. If one third of A’s income exceeds one fourth of C's income by ₹ 1000, what is B’s income in ?
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A : B = 3 : 2 = 9 : 6
B : C = 3 : 2 = 6 : 4
∴ A : B : C = 9 : 6 : 4∴ 9x − 4x = 1000 3 4
⇒ 3x – x = 1000
⇒ 2x = 1000
⇒ x = 500
∴ B’s income = 6x = 6 × 500
= ₹ 3000Correct Option: A
A : B = 3 : 2 = 9 : 6
B : C = 3 : 2 = 6 : 4
∴ A : B : C = 9 : 6 : 4∴ 9x − 4x = 1000 3 4
⇒ 3x – x = 1000
⇒ 2x = 1000
⇒ x = 500
∴ B’s income = 6x = 6 × 500
= ₹ 3000
- Monthly income of A and B are in the ratio of 4 : 3 and their expenses bear the ratio 3 : 2. Each of them saves ₹ 6,000 at the end of the month, then the monthly income of A is
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Let the monthly income of A and B be ₹ 4x and ₹ 3x respectively and their expenditures be ₹ 3y and Rs. 2y respectively.
∴ 4x – 3y = 6000
and 3x – 2y = 6000
⇒ 4x – 3y = 3x – 2y
⇒ x = y
∴ 4x – 3y = 6000
⇒ x = 6000
⇒ A’s monthly income = 4x
= ₹ 24000Correct Option: B
Let the monthly income of A and B be ₹ 4x and ₹ 3x respectively and their expenditures be ₹ 3y and Rs. 2y respectively.
∴ 4x – 3y = 6000
and 3x – 2y = 6000
⇒ 4x – 3y = 3x – 2y
⇒ x = y
∴ 4x – 3y = 6000
⇒ x = 6000
⇒ A’s monthly income = 4x
= ₹ 24000
- The ratio of the income to the expenditure of a family is 10 : 7. If the family’s expenses are ₹ 10,500, then savings of the family is
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Income of the family
= 10 × 10500 = ₹ 15000 7
Savings = 15000 – 10500
= ₹ 4500Correct Option: A
Income of the family
= 10 × 10500 = ₹ 15000 7
Savings = 15000 – 10500
= ₹ 4500
- The ratio of income and expenditure of a person is 11 : 10. If he saves ₹ 9,000 per annum, his monthly income is
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Let the income of man be ₹ = 11x and his expenditure be ₹ 10x
∴ Savings = x = ₹ 9000
∴ Monthly income of man= 11 × 9000 = ₹ 8250 12 Correct Option: D
Let the income of man be ₹ = 11x and his expenditure be ₹ 10x
∴ Savings = x = ₹ 9000
∴ Monthly income of man= 11 × 9000 = ₹ 8250 12
