type 4 income & expenditure based ratio & proportion problems Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Let the income of two persons be Rs.5x and Rs.3x respectively

and their expenditures be Rs.9y and Rs.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

$x = 3200/2$ = 1600

First person’s income

= Rs.(1600 × 5) = Rs.8000

Second person’s income

= 3x = Rs.(1600 × 3) = Rs.4800

Answer: (d)

Let the income of A, B and C be Rs.3x, Rs.7x and Rs.4x respectively

and their expenses be Rs.4y, Rs.3y and Rs.5y respectively.

3x = 2400

x = 800

4y = 2400 - 300 = 2100

y = 525

B’s saving

= (7x - 3y)

= Rs.(7 × 800 - 3 × 525)

= Rs.(5600 - 1575) = Rs.4025

and C’s savings = Rs.(4x - 5y)

= Rs.(3200 - 2625) = Rs.575

Answer: (d)

A : B = 3 : 2 = 9 : 6

B : C = 3 : 2 = 6 : 4

A : B : C = 9 : 6 : 4

${9x}/3 - {4x}/4$= 1000

3x - x = 1000

2x = 1000

x = 500

B’s income = 6x

= 6 × 500 = Rs.3000

Answer: (d)

Let the income of A and B be Rs.5x and Rs.3x respectively.

Let the expenses of A, B and C be Rs.8y, Rs.5y and Rs.2y respectively.

Then, 2y = 2000

$y =2000/2 = 1000$

B saves = Rs.700

3x - 5y = 700

3x - 5×1000 = 700

3x = 700 +5000 = 570

$x = 5700/3 = 1900$

A’s saving = Rs.(5x - 8y)

= Rs.(5×1900 - 8×1000)

= Rs.(9500 - 8000) = Rs.1500

Answer: (a)

Let the income of two persons (A and B) be Rs.2x and Rs.3x respectively.

Again let the expenditures of A and B be Rs.5y and Rs.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 = Rs.1600

B’s income = 3x

= 3 × 800 = Rs.2400

Answer: (a)

Income of A and B

= Rs.6x and 5x

Expenses of A and B

= Rs.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 = Rs.2200