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

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The following question based on ratio & proportion topic of quantitative aptitude

Questions : The incomes of A and B are in the ratio 3 : 2 and their expenditures are in the ratio 5 : 3. If each saves Rs.1000, then A’s income is

(a) Rs.2000

(b) Rs.5000

(c) Rs.4000

(d) Rs.6000

The correct answers to the above question in:

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,

6x-10y=2000
6x-9y=3000
-+-
-y=-1000

y = 1000

From equation (i),

3x - 5 × 1000 = 1000

3x = 1000 + 5000

= Rs.6000 = A’s income

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Read more income and expenditure based ratio and proportion Based Quantitative Aptitude Questions and Answers

Question : 1

A man spends a part of his monthly income and saves the rest. The ratio of his expenditure to the savings is 61 : 6. If his monthly income is Rs.8710, the amount of his monthly savings is

a) Rs.980

b) Rs.780

c) Rs.690

d) Rs.870

Answer: (b)

Expenditure : Savings

= 61 : 6

Sum of the terms of ratio

= 61 + 6 = 67

Total monthly salary

= Rs.8710

Monthly savings

= Rs.$(6/67 × 8710)$ = Rs.780

Question : 2

Ratio between the monthly incomes of A and B is 9 : 8 and the ratio between their expenditures is 8 : 7. If they save Rs.500 each, find A’s monthly income.

a) Rs.4,500

b) Rs.5,000

c) Rs.4,000

d) Rs.3,500

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

Question : 3

The ratio of income of two persons is 5 : 3 and that of their expenditures is 9 : 5. Find the income of each person, if they save Rs.1,300 and Rs.900 respectively.

a) Rs.5,000, Rs.3,000

b) Rs.4,500 Rs.2,700

c) Rs.3,000, Rs.1,800

d) Rs.4,000, Rs.2,400

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

27x-45y=8100
25x-45y=6500
-+-
2x=1600

x = 800

Now, income of first person

= 5x = 5 × 800 = Rs.4000

and that of second person

= 3x = 3 × 800 = Rs.2400

Question : 4

Incomes of x and y are in the ratio 4:3. Their expenditures are in the ratio 12:7. Both save Rs.3200 at the end of the month, then the income of x is

a) Rs.2000

b) Rs.4000

c) Rs.6000

d) Rs.8000

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,

7a-21b=5600
9a-21b=9600
-+-
-2a=-4000

a = 2000

x’s income = 4a

= 4 × 2000 = Rs.8000

Question : 5

The ratio of the income to the expenditure of a family is 10 : 7. If the family’s expenses are Rs.10,500, then savings of the family is

a) Rs.4, 000

b) Rs.5, 000

c) Rs.10, 000

d) Rs.4, 500

Answer: (d)

Income of the family

= $10/7 × 10500$ = Rs.15000

Savings = 15000 - 10500

= Rs.4500

Question : 6

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 :

a) 99 : 56 : 69

b) 99 : 69 : 56

c) 69 : 56 : 99

d) 56 : 99 : 69

Answer: (d)

Income of A = Rs.7x ;

B = Rs.9x and C = Rs.12x

Expenses of A = Rs.8y ;

B = Rs.9y and C = Rs.15y

7x - 8y = $1/4$ × 7x

7x - ${7x}/4$ = 8y

${21x}/4 = 8y$

21x = 32y.

A’s saving = $1/4 × 7x$

= $1/4 × 32/3 y = 8/3 y$

B’s saving = 9x - 9y

= $9 × 32/21 y - 9y$

= ${96y - 63y}/7 = {33y}/7$

C’s saving = 12 x - 15 y

= 12 × $32/21$ y - 15y

= ${128y - 105y}/7 = {23y}/7$

Required ratio

= $8/3y : 33/7y : 23/7y$

= 56 : 99 : 69

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