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

Answer: (a)

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

Answer: (d)

Let income of two persons be 5x and 3x.

and their expenses be 9y and 5y respectively.

Then, 5x - 9y = 1300 ...(i)

and 3x - 5y = 900 ...(ii)

By 9 × (ii) - 5 × (i), we get

x = 800

Now, income of first person

= 5x = 5 × 800 = Rs.4000

and that of second person

= 3x = 3 × 800 = Rs.2400

Answer: (c)

Let the income of A be Rs.5x

and that of B be Rs.6x.

According to the question,

6x - 5x =1100

x = 1100

Total income

= 5x + 6x = Rs.11x

= Rs.(11×1100) = Rs.12100

Answer: (d)

Let incomes of A and B be Rs.3x and Rs.2x respectively.

Let the expenditures of A and B be Rs.5y and Rs.3y respectively.

According to the question,

3x - 5y = Rs. 1000 ... (i)

2x - 3y = Rs. 1000 ... (ii)

By equation (i) × 2 - (ii) × 3,

y = 1000

From equation (i),

3x - 5 × 1000 = 1000

3x = 1000 + 5000

= Rs.6000 = A’s income

Answer: (d)

x’s income = Rs.4a

y’s income = Rs.3a

x’s expenditure = Rs.12b

y’s expenditure = Rs.7b

4a - 12b = 3200

a - 3b = 800 ...(i)

Again, 3a - 7b = 3200 ...(ii)

By equation (i) × 7 - (ii) × 3,

a = 2000

x’s income = 4a

= 4 × 2000 = Rs.8000

Answer: (d)

Income of the family

= $10/7 × 10500$ = Rs.15000

Savings = 15000 - 10500

= Rs.4500