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

Question : 6 [SSC MTS 2011]

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 : 7 [SSC CGL Prelim 2002]

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 : 8 [SSC CGL Prelim 2007]

The ratio of incomes of A and B is 5 : 6. If A gets Rs.1,100 less than B, their total income (in rupees) is

a) 14,400

b) 10,000

c) 12,100

d) 9,900

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

Question : 9 [SSC CGL Tier-1 2011]

The ratio of weekly income of A and B is 9 : 7 and the ratio of their expenditures is 4 : 3. If each saves Rs.200 per week, then the sum of their weekly income is

a) Rs.4,800

b) Rs.5,600

c) Rs.3,200

d) Rs.3,600

Answer: (c)

Let A’s and B’s weekly income be Rs.9x and Rs.7x

and their expenditures be Rs.4y and Rs.3y respectively.

Then, 9x - 4y = 200 ...(i)

and 7x - 3y = 200 ...(ii)

9x - 4y = 7x - 3y

9x - 7x = 4y - 3y

2x = y ...(iii)

From equation (i),

9x - 4y = 200

9x - 8x = 200

x = 200

Sum of their weekly income

= 16x = 16 × 200 = Rs.3200

Question : 10 [SSC CGL Prelim 2002]

A and B have monthly incomes in the ratio 5 : 6 and monthly expenditures in the ratio 3 : 4. If they save Rs.1800 and Rs.1600 respectively, find the monthly income of B :

a) Rs.1720

b) Rs.7200

c) Rs.2700

d) Rs.3400

Answer: (b)

Given

$\text”Monthly income of A”/ \text”Monthly income of B” = 5/6$

Monthly income of A = 5x

and that of B = 6x (x is a constant)

According to the question

${5x - 1800}/{6x - 1600} =3/4$

20x - 7200 = 18x - 4800

2x = 2400 ⇒ x = 1200

Monthly income of B

= 1200 × 6 = Rs.7200

IMPORTANT quantitative aptitude EXERCISES

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