Ratio, Proportion
- The ratio of monthly incomes of A, B is 6 : 5 and their monthly expenditures are in the ratio 4 : 3. If each of them saves ₹ 400 per month, find the sum of their monthly incomes.
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Income of A and B = ₹ 6x and 5x
Expenses of A and B = ₹ 4y and 3y
∴ 6x – 4y = 400 ...(i)
5x – 3y = 400 ...(ii)
By equation (i)× 3 – (ii) × 4
⇒ 18x – 12y –20x + 12y
= 1200 – 1600
⇒ 2x = 400 ⇒ x = 200
∴ Total income
= 6x + 5x = 11x = ₹ 2200Correct Option: C
Income of A and B = ₹ 6x and 5x
Expenses of A and B = ₹ 4y and 3y
∴ 6x – 4y = 400 ...(i)
5x – 3y = 400 ...(ii)
By equation (i)× 3 – (ii) × 4
⇒ 18x – 12y –20x + 12y
= 1200 – 1600
⇒ 2x = 400 ⇒ x = 200
∴ Total income
= 6x + 5x = 11x = ₹ 2200
- Annual incomes of Amit and Veeri are in the ratio 3:2, while the ratio of their expenditure is 5 : 3. If at the end of the year each saves ₹ 1,000, the annual income of Amit is
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Amit’s income = ₹ 3x and his expenditure = ₹ 5y
Veeri’s income = ₹ 2x and his expenditure = ₹ 3y
∴ 3x – 5y = 2x – 3y
⇒ x = 2y
∴ 3x – 5y = 1000
⇒ 6y – 5y = 1000 ⇒ y = 1000
∴ x = 2000
∴ Amit’s income
= 3x = 3 × 2000 = ₹ 6000Correct Option: D
Amit’s income = ₹ 3x and his expenditure = ₹ 5y
Veeri’s income = ₹ 2x and his expenditure = ₹ 3y
∴ 3x – 5y = 2x – 3y
⇒ x = 2y
∴ 3x – 5y = 1000
⇒ 6y – 5y = 1000 ⇒ y = 1000
∴ x = 2000
∴ Amit’s income
= 3x = 3 × 2000 = ₹ 6000
- If the annual income of A, B and C are in the ratio 1 : 3 : 7 and the total annual income of A and C is ₹
8,00,000, then the monthly salary of B (in ₹ ) is
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Let Annual Income of A, B and C be x, 3x and 7x
x + 7x = 800000
⇒ 8x = 800000
⇒ x = 100000
∴ B’s monthly income= 100000 × 3 12
= ₹ 25000Correct Option: B
Let Annual Income of A, B and C be x, 3x and 7x
x + 7x = 800000
⇒ 8x = 800000
⇒ x = 100000
∴ B’s monthly income= 100000 × 3 12
= ₹ 25000
- Ratio between the monthly incomes of A and B is 9 : 8 and the ratio between their expenditures is 8 : 7. If they save ₹ 500 each, find A’s monthly income.
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If the ratio of the income of A and B be a : b and that of their expenses be c : d and each saves ₹ x, then,
A’s income = ax(d − c) ad − bc = 9 × 500(7 − 8) 9 × 7 − 8 × 8
= 9 × 500 = ₹ 4500Correct Option: C
If the ratio of the income of A and B be a : b and that of their expenses be c : d and each saves ₹ x, then,
A’s income = ax(d − c) ad − bc = 9 × 500(7 − 8) 9 × 7 − 8 × 8
= 9 × 500 = ₹ 4500
- Incomes of A and B are in the ratio 4 : 3 and their annual expenses in the ratio 3 : 2. If each saves ₹ 60,000 at the end of the year, the annual income of A is
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Let the annual income of A and B be ₹ 4x and ₹ 3x and their income be Rs. 3y and Rs. 2y. respectively.
∴ 4x – 3y = 60000 ...(i)
and 3x – 2y = 60000 ...(ii)
Clearly, 4x – 3y = 3x – 2y
⇒ x = y
From equation (i),
x = 60000
∴ A’s annual income
= 4x = 4 × 60000
= ₹ 240000Correct Option: C
Let the annual income of A and B be ₹ 4x and ₹ 3x and their income be Rs. 3y and Rs. 2y. respectively.
∴ 4x – 3y = 60000 ...(i)
and 3x – 2y = 60000 ...(ii)
Clearly, 4x – 3y = 3x – 2y
⇒ x = y
From equation (i),
x = 60000
∴ A’s annual income
= 4x = 4 × 60000
= ₹ 240000
