type 4 income & expenditure based ratio & proportion problems Practice Questions Answers Test with Solutions & More Shortcuts

Question : 1 [SSC CGL Tier-I 2011]

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

Question : 2 [SSC CGL Tier-1 2011]

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 : 3 [SSC CAPFs SI 2015]

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 : 4 [SSC CGL Tier-I 2015]

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

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

Question : 5 [SSC CGL Tier-I 2016]

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

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