Ratio Proportion Practice Questions

1) Question: The ratio of expenditure to savings of Rajesh is 2:1 and 25% of the income of Nallu is equal to 40% of his income of Rajesh. If the expenditure of Nallu is double the expenditure of Rajesh, then the savings of Nallu is what percentage of the savings of Rajesh?
A.70%
B.30%
C.80%
D.None of these

Answer: C

Solution: 

Let the income of Rajesh = 100x And the income of Nallu = 100x*40/25 = 160x
The expenditure of Rajesh = 100x*2/(2+1) = 200x/3
The savings of Rajesh = 100x-200x/3 = 100x/3
The expenditure of Nallu = 200x/3 *2 = 400x/3
The savings of Nallu = 160x-400x/3 = 80x/3
Required percentage = (80x/3)/(100x/3)*100 = 80/100*100 = 80% 

2) Question: The ratio of the total number of male and females in a company is 4:5. If 18 employees resigned from the company and 12 new male employees and 10 new female employees joined the company, then the ratio becomes 14:15. Find the initial number of employees in the company.

A.89
B.54
C.65
D.None of these

Answer: B

Solution:

The initial number of male employees = 4x
The initial number of female employees = 5x
(4x - 18 * 4/9 + 12)/(5x - 18 * 5/9 + 10) = 14/15
(4x + 4)/5x = 14/15
60x + 60 = 70x
x = 6
Total number of employees in the company = 4* 6 + 5 * 6 = 54

3) Question: The income of Gokila is 25% less than that of Shri and the expenditure of Gokila is 12.5% more than that of Shri. If the savings of Shri and Gokila is Rs.6000 and Rs.3000 respectively, then find the expenditure of Gokila.

A.Rs.4500
B.Rs.6300
C.Rs.5400
D.Rs.3600
E.None of these

Answer: A

Solution:

The ratio of the income of Gokila to Shri = 75:100 = 3:4
The ratio of the expenditure of Gokila to Shri = 112.5:100 = 9:8
3x – 9y = 3000 ---(1)
4x – 8y = 6000 ---(2)
From (1) and (2),
12x – 36y = 12000
- 12x + 24y = - 18000
12y = 6000
y = 500
The expenditure of Gokila = 9 * 500 = Rs.4500

4) Question: The Ratio of the income to the expenditure of A and B is 5:4 and 8:7 respectively and the sum of their savings is Rs.9000 and the savings of A is Rs.1000 more than that of B. Find the difference between their incomes.

A.Rs.7000
B.Rs.4500
C.Rs.6000
D.Rs.8000
E.None of these

Answer: A

Solution: 
Income of A = 5x
Expenditure of A = 4x
Savings of A = 5x – 4x = x
Income of B = 8y
Expenditure of B = 7y
Savings of B = 8y – 7y = y
x + y = 9000 ---- (1)

x – y = 1000 ---- (2)
From (1) and (2),
2x = 10000
x = 5000
y = 5000 – 1000 = 4000
Income of A = 5 * 5000 = Rs.25000
Income of B = 8 * 4000 = Rs.32000
Required difference = 32000 – 25000 = Rs.7000

5) Question: The income of Gray is 125% of the income of Parker and the income of Robert is 50% more than that of Parker. If the difference between the income of Gray and Robert is Rs.2100, then find the income of Parker.
A.Rs.8400
B.Rs.7200
C.Rs.9600
D.Rs.8200
E.None of these

Answer: A

Solution: 
Let the income of Parker = x
Income of Gray =125x/100
Income of Robert = 150x/100
(150x/100) – (125x/100 )= 2100
25x = 2100 * 100
x = 8400 

6) Question: Incomes of John and Kelvin are in the ratio of 4:7 and their spending are in the ratio of 6:11. If John saves one-third of his income, then what will be the ratio of their savings?

A. 12:13

B. 13:12

C. 18:19

D. 12:19

E. None of these

Answer: D

Solution: 

Let the income of
John 4x, Kelvin 7x
And expenditure be:
John → 6y……..(i)
Kelvin → 11y
John spending = John’s earning – John’s savings
John’s expenditure = 4x – 4x/3 = 8/3 x .............(ii)
(i) = (ii)
6y = 8/3 x ⇒ x/y = 9/4

Reqd. Ratio = 4x-6y / 7x-11y 

= 4x-(4/9 x)6 / 7x-(4/9 x)11

=36 – 24 / 63 – 44 = 12/19

= The answer is 12:19

7) Question: Cost of a pen , marker and sharpener is rupees 15, 18 and 5 respectively. To increase his sales the shopkeeper sells sets of 5 pens and 3 markers for Rs. 100. Find the amount paid by the customer if he buys 15 pens, 10 marker and 2 sharpeners.
A. Rs. 338

B. Rs. 346

C. Rs. 328

D. Rs. 367

E. None of these

Answer: C

Solution:

Cost of Pen (P) = Rs 15
Cost of Marker(M) = Rs 18
Cost of Sharpener(S) = Rs 5
He sells a set of 5 pens and 3 markers for Rs 100 (This is not the cost price, he sells this set at a lower price just to increase sales)
5P + 3M = 100 …….I
3 × (5P + 3M = 100)
15P + 9M = 300
Multiplying I by 3 we get the cost of 15 pens and 9 markers = Rs 300
The remaining 1 marker and 2 sharpeners are not part of the set and they have to be bought separately at a cost price
Cost of 1 Marker and 2 Sharpener = 18 + 10 = 28
Therefore, the cost of 15 pens 10 markers, and 2 sharpeners = 300 + 28 = Rs 328
Hence, option C is correct.

8) Question: The income of A is 40% less than the income of B and the expenditure of A is 40% of B’s expenditure. If the income of A is 70% of the expenditure of B then find the ratio between the saving of A and B.
A. 8:15
B. 9:5
C. 9:25
D. 7:13

Answer: B

Solution:
Let the income of B is 100x
Then income of A is 60x
Let expenditure of B is 100y
Then expenditure of A is 40y
Given, the income of A is 70% of the expenditure of B
60x = (70/100)100y
6x = 7y
Saving of A/Saving of B = (60x – 40y)/(100x – 100y)
Put the value of x in above
= (70y – 40y)/((700y/6) – 100y)
=30y/(100y/6)
=9/5 = 9:5

9) Question: If A: B: C: D = 4: 6: 7: 9 and A + C = 3454 then find the sum of A and B.

A. 3250
B. 3140
C. 3540
D.3658

Answer: B
Solution:
A: B: C: D = 4: 6: 7: 9
A + C = 4x + 7x = 11x
3454 = 11x
X = 3454/11
= 314
A + B = 4x + 6x = 10x
= 10(314)
= 3140

10) Question: Total income of A and B is Rs.5000 if A saves 20% and B saves 30% and their savings are in the ratio 4:9. Find their individual income.
A. 1500, 3500
B. 1700, 3300
C.1000, 4000
D. 2000, 3000

Answer: D

Solution: 

Let the income of A and B is x and y
X + y = 5000 -------- (1)
20%x : 30%y = 4 : 9
x/5 : 3y/10 = 4 : 9
2x : 3y = 4 : 9
x/y = 2/3
Put the value of x in (1)
2y/3 + y = 5000
5y/3 = 5000
Y = 3000
X = 5000 – 3000 = 2000

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