Ratio, Proportion
- A person bought some rice and wheat for ₹ 380. The ratio of weight of rice and wheat is 4 : 3 and the price of equal amount of rice and wheat is in the ratio 5 : 6. The rice was bought of worth
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Rice : Wheat
= 4 × 5 : 3 × 6
= 20 : 18 = 10 : 9
∴ Total cost of rice= 10 × 380 = ₹ 200 19 Correct Option: C
Rice : Wheat
= 4 × 5 : 3 × 6
= 20 : 18 = 10 : 9
∴ Total cost of rice= 10 × 380 = ₹ 200 19
- The monthly income of two persons are in the ratio 2 : 3 and their monthly expenses are in the ratio 5 : 9. If each of them saves ₹ 600 per month, then their monthly incomes are
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Let the income of two persons (A and B) be ₹ 2x and ₹ 3x respectively. Again let the expenditures of A and B be ₹ 5y and ₹ 9y respectively.
∴ 2x– 5y = 600 ...(i)
3x – 9y = 600 ...(ii)
From equations (i) and (ii),
2x – 5y = 3x – 9y
⇒ x = 4y
From equation (i),
2 × 4y – 5y = 600
⇒ 3y = 600
= y = 200
∴ x = 4 × 200 = 800
∴ A’s income = 2x = 2 × 800
= ₹ 1600
B’s income = 3x = 3 × 800
= ₹ 2400Correct Option: C
Let the income of two persons (A and B) be ₹ 2x and ₹ 3x respectively. Again let the expenditures of A and B be ₹ 5y and ₹ 9y respectively.
∴ 2x– 5y = 600 ...(i)
3x – 9y = 600 ...(ii)
From equations (i) and (ii),
2x – 5y = 3x – 9y
⇒ x = 4y
From equation (i),
2 × 4y – 5y = 600
⇒ 3y = 600
= y = 200
∴ x = 4 × 200 = 800
∴ A’s income = 2x = 2 × 800
= ₹ 1600
B’s income = 3x = 3 × 800
= ₹ 2400
- The ratio of income of two persons is 5 : 3 and that of their expenditures is 9 : 5. If they save ₹ 2600 and ₹ 1800 respectively, their incomes are :
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Let the income of two persons be ₹ 5x and ₹ 3x respectively and their expenditures be ₹ 9y and ₹ 5y respectively.
As given,
5x – 9y = 2600 ...(i)
3x – 5y = 1800 ...(ii)
By 5 × (i) – 9 × (ii) we get
25x – 27x = 13000 – 16200
⇒ – 2x = – 3200⇒ x = 3200 = 1600 2
∴ First person’s income
= ₹ (1600 × 5) = ₹ 8000
Second person’s income
= 3x = ₹ (1600 × 3)
= ₹ 4800Correct Option: A
Let the income of two persons be ₹ 5x and ₹ 3x respectively and their expenditures be ₹ 9y and ₹ 5y respectively.
As given,
5x – 9y = 2600 ...(i)
3x – 5y = 1800 ...(ii)
By 5 × (i) – 9 × (ii) we get
25x – 27x = 13000 – 16200
⇒ – 2x = – 3200⇒ x = 3200 = 1600 2
∴ First person’s income
= ₹ (1600 × 5) = ₹ 8000
Second person’s income
= 3x = ₹ (1600 × 3)
= ₹ 4800
- The monthly salaries of A, B and C are in the ratio 2 : 3 : 5. If C’s monthly salary is ₹ 12,000 more than that of A, then B’s annual salary is
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Let the monthly salary of A, B & C be 2x, 3x and 5x
now, 5x – 2x = 12,000
⇒ 3x = 12000 or x = 4000
∴ Monthly salary of B = 3 × 4000
= 12,000
⇒ Annual salary of B
= 12000 × 12 = ₹ 144000Correct Option: B
Let the monthly salary of A, B & C be 2x, 3x and 5x
now, 5x – 2x = 12,000
⇒ 3x = 12000 or x = 4000
∴ Monthly salary of B = 3 × 4000
= 12,000
⇒ Annual salary of B
= 12000 × 12 = ₹ 144000
- A man spends a part of his monthly income and saves a part of it. The ratio of his expenditure to his saving is 26 : 3. If his monthly income is ₹ 7250, what is the amount of his monthly savings ?
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Let his expenditures be ₹ 26x and savings be ₹ 3x.
∴ 26x + 3x = 7250
⇒ 29x = 7250⇒ x = 7250 = 250 29
∴ Savings = 3x = ₹ 750Correct Option: C
Let his expenditures be ₹ 26x and savings be ₹ 3x.
∴ 26x + 3x = 7250
⇒ 29x = 7250⇒ x = 7250 = 250 29
∴ Savings = 3x = ₹ 750
