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
(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
Practice ratio & proportion (type 4 income & expenditure based ratio & proportion problems) Online Quiz
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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 »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 »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 »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 »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 »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 »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
GET ratio & proportion PRACTICE TEST EXERCISES
type 1 basic concepts of ratio & proportion
type 2 age based ratio & proportion problems
type 3 addition subtraction product on ratio & proportion
type 4 income & expenditure based ratio & proportion problems
type 5 shares & partnership based ratio & proportion problems
type 6 fractions based ratio & proportion problems
type 7 finding sum difference product based ratio & proportion problems
type 8 alligation & mixtures based ratio & proportion problems
type 9 coins & rupees based ratio & proportion problems
ratio & proportion Shortcuts and Techniques with Examples
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