Ratio, Proportion
- 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
- The ratio of income of P and Q is 3 : 4 and the ratio of their expenditures is 2 : 3. If both of them save ₹ 6000, the income of P is
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Let the income of P and Q be ₹ 3x and 4x respectively.
Again, let their expenditures be ₹ 2y and 3y respectively.
According to the question.
3x – 2y = 6000 ...(i)
and 4x – 3y = 6000 ...(ii)
From equations (i) and (ii)
3x – 2y = 4x – 3y
or, 4x – 3x = 3y – 2y
or, x = y
From equation (i),
⇒ 3x – 2x = 6000
x = 6000
The income of P = ₹ 3x
= ₹ (3 × 6000) = ₹ 18000Correct Option: C
Let the income of P and Q be ₹ 3x and 4x respectively.
Again, let their expenditures be ₹ 2y and 3y respectively.
According to the question.
3x – 2y = 6000 ...(i)
and 4x – 3y = 6000 ...(ii)
From equations (i) and (ii)
3x – 2y = 4x – 3y
or, 4x – 3x = 3y – 2y
or, x = y
From equation (i),
⇒ 3x – 2x = 6000
x = 6000
The income of P = ₹ 3x
= ₹ (3 × 6000) = ₹ 18000
- The income of A, B and C are in the ratio 7 : 9 : 12 and their spendings are in the ratio 8 : 9 : 15. If A saves (1/4)th of his income, then the savings of A, B and C are in the ratio of :
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Income of A = ₹ 7x ;
B = ₹ 9x and C = ₹ 12x
Expenses of A = ₹ 8y ;
B = ₹ 9y and C = ₹ 15y∴ 7x – 8y = 1 × 7x 4 ⇒ 7x – 7x = 8y 4 ⇒ 21x = 8y ⇒ 21x = 32y. 4 ∴ A’s saving = 1 × 7x 4 = 1 × 32 y = 8 y 4 3 3
B’s saving = 9x – 9y= 9 × 32 y − 9y 21 = 96y − 63y 7 = 33y 7
C’s saving = 12 x – 15 y= 12 × 32 y − 15y 21 = 128y − 105y 7 = 23y 7
∴ Required ratio= 8 y : 33 y : 23 y 3 7 7
= 56 : 99 : 69Correct Option: A
Income of A = ₹ 7x ;
B = ₹ 9x and C = ₹ 12x
Expenses of A = ₹ 8y ;
B = ₹ 9y and C = ₹ 15y∴ 7x – 8y = 1 × 7x 4 ⇒ 7x – 7x = 8y 4 ⇒ 21x = 8y ⇒ 21x = 32y. 4 ∴ A’s saving = 1 × 7x 4 = 1 × 32 y = 8 y 4 3 3
B’s saving = 9x – 9y= 9 × 32 y − 9y 21 = 96y − 63y 7 = 33y 7
C’s saving = 12 x – 15 y= 12 × 32 y − 15y 21 = 128y − 105y 7 = 23y 7
∴ Required ratio= 8 y : 33 y : 23 y 3 7 7
= 56 : 99 : 69
- The annual income of A and B are in the ratio 4 : 3 and the ratio of their expenditures is 3 : 2. If each of them saves ₹ 600 in the year, the annual income of A is
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Let the annual income of A and B be ₹ 4x and 3x respectively. Also let their annual expenditures be ₹ 3y and 2y respectively
According to question,
4x – 3y = 600 ...(i)
3x – 2y = 600 ...(ii)
From equation (i) and (ii)
4x –3y = 3x – 2y ⇒ x = y
From equation (i)
4x – 3x = 600 ⇒ x = 600
Annual income of A
= 4x = 4 × 600 = ₹ 2400Correct Option: D
Let the annual income of A and B be ₹ 4x and 3x respectively. Also let their annual expenditures be ₹ 3y and 2y respectively
According to question,
4x – 3y = 600 ...(i)
3x – 2y = 600 ...(ii)
From equation (i) and (ii)
4x –3y = 3x – 2y ⇒ x = y
From equation (i)
4x – 3x = 600 ⇒ x = 600
Annual income of A
= 4x = 4 × 600 = ₹ 2400
