Ratio, Proportion
- The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio 8 : 5 : 2. If C spends ₹ 2000 and B saves ₹ 700, then A saves
-
View Hint View Answer Discuss in Forum
Let the income of A and B be ₹ 5x and ₹ 3x respectively.
Let the expenses of A, B and C
be ₹ 8y, Rs. 5y and ₹ 2y respectively. Then,
2y = 2000⇒ y = 2000 = 1000 2
B saves = ₹ 700
∴ 3x –5y = 700
⇒ 3x –5×1000 = 700
⇒ 3x = 700 +5000 = 5700⇒ x = 5700 = 1900 3
∴ A’s saving = ₹ (5x–8y)
= ₹ (5×1900–8×1000)
= ₹ (9500 – 8000) = ₹ 1500Correct Option: A
Let the income of A and B be ₹ 5x and ₹ 3x respectively.
Let the expenses of A, B and C
be ₹ 8y, Rs. 5y and ₹ 2y respectively. Then,
2y = 2000⇒ y = 2000 = 1000 2
B saves = ₹ 700
∴ 3x –5y = 700
⇒ 3x –5×1000 = 700
⇒ 3x = 700 +5000 = 5700⇒ x = 5700 = 1900 3
∴ A’s saving = ₹ (5x–8y)
= ₹ (5×1900–8×1000)
= ₹ (9500 – 8000) = ₹ 1500
- The ratio of incomes of A and B is 5 : 6. If A gets ₹ 1,100 less than B, their total income (in rupees) is
-
View Hint View Answer Discuss in Forum
Let the income of A be ₹ 5x and that of B be ₹ 6x.
According to the question,
6x –5x =1100
∴ Total income = 5x + 6x = ₹ 11x
= ₹ (11×1100) = ₹ 12100Correct Option: B
Let the income of A be ₹ 5x and that of B be ₹ 6x.
According to the question,
6x –5x =1100
∴ Total income = 5x + 6x = ₹ 11x
= ₹ (11×1100) = ₹ 12100
- 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
-
View Hint View Answer Discuss in Forum
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
-
View Hint View Answer Discuss in Forum
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 :
-
View Hint View Answer Discuss in Forum
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
