Quantitative Aptitude Word Problems | IBPS | Insurance Exams

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Quantitative Aptitude Word Problems | IBPS | Insurance Exams
1. A and B can complete a certain piece of work in some days individually. A is 4 times as efficient as B. They have together done the work for 10 days then A leaves, B works for 2 more days. Total 75% of work is completed in this way. In how many days can A finish the work alone?
a) 9 1/3 days
b) 6 2/3 days
c) 17 1/3 days
d) 19 2/3 days
e) 14 2/7 days
2. Two person A and B are standing at point P and Q respectively. They both started to travel towards each other. Ratio of speed of A and B is 2 : 3. If A travels for 2 hour and B for 3 hours it is found that one has travelled 50 km more than the other. Find the sum of speeds of both. A and B
a) 50 km/h
b) 40 km/h
c) 60 km/h
d) 55 km/h
e) 35 km/h
3. Sweta and Neha profess to tell their present ages as 25 and 20 years respectively. (Not original age). Ratio of their original ages 5 year ago is 5 : 4. Sum of ages of both 5 years hence is 400/9% more than the sum of present ages of both professed by them. Find the sum of their present original age
a) 25
b) 35
c) 55
d) 40
e) 50
4. A person buys some articles. He sold 40% of articles at 20% profit and remaining at 33 1/3% profit. If percent profit is calculated on selling price then what is the ratio of selling price of articles sold at 20% profit to the articles sold at 33 1/3% profit
a) 4 : 5
b) 7 : 9
c) 5 : 1
d) 2 : 3
e) 5 : 9
5. The average salary of A, B and C is 18000 per month and that of B, C and D is Rs. 24000 per month. If the salary of D is thrice that of A, then the average salary of B + C is
a) 18,200
b) 22,000
c) 22,500
d) 19,800
e) 20,000
6. Ritesh travels the first part of his journey at 20 km/hr and the next at 70 km/hr, covering the entire journey at an average speed of 50 km/hr. What is the ratio of the distance that he covered at 20 km/hr to that he covered at 70 km/hr ?
a) 5 : 7
b) 4 : 7
c) 3 : 5
d) 4 : 21
e) None of these
7. The ratio between the sides of a room is 3 : 2. The cost of white washing the celling of the room at Rs 10 per square metre is Rs 6000 and the cost of papering the walls at Rs 4 per square metre is Rs 1920. The height of the room is ?
a) 5.6 m
b) 5.8 m
c) 4.8 m
d) 6.5 m
e) 8.5 m
8. Present age of a father is three times more than his son. 8 years hence, father’s age will be 2 and a half times of his son’s age. After 8 more years, how many times would father be his son’s age ?
a) 2 times
b) 3 times
c) 4 times
d) 2 ½ times
e) None of these
9. Ankit sold his car to Bittu at a profit of 20% and Bittu sold it Chintu at a profit of 10%. Chintu sold it to mechanic at a loss of 9.09%. Mechanic spent 10% of his purchasing price and then sold it at a profit of 8.33% to Ankit once again. What is the loss of Ankit ?
a) 28%
b) 32%
c) 18%
d) 23%
e) 40%
10. A mixture containing milk and water in the ratio 3 : 2 and another mixture contains them in the ratio 4 : 5. How many litres of the later must be mixed with 3 litres of the former so that the resulting mixture may contain equal quantities of milk and water ?
a) 3.5 litres
b) 5.4 litres
c) 3.2 litres
d) 5.2 litres
e) None of these
11. The sum of three numbers is 123. If the ratio between first and second numbers is 2 : 5 and that of between second and third is 3 : 4, then find the difference between second and the third number.
a) 15
b) 25
c) 20
d) 12
e) None of these
12. Bhattji started a business with an initial capital of  Rs. 1.5 lakh. After a few months, Radhe joined his business with a capital of Rs. 1 lakh. The profits at the end of the year were divided among them in the ratio of 3:1. After how many months did Radhe join the business?
a) 3
b) 4
c) 5
d) 6
e) 7
13. Mohit invested some amount in a bank at a simple interest and got Rs. 2365 after 3 years. If he invested the same money with same interest in the bank for 5 years then he would have got Rs. 2655. Find out rate of interest offered by the bank and the money invested by Mohit respectively?
a) 7 %, Rs 2020
b) 7.5%, Rs 1930
c) 8.5%, Rs 1890
d) 8%, Rs 1830
e) None of These
14. The ratio of the turnover of two companies, XYZ and ABC is 9:8 and the ratio of their expenditures is 17: 15 respectively. Profit is calculated as the difference between turnover and expenditure. If each of the companies posted a profit of 2500, what will be the difference between turnover of XYZ and expenditure of ABC?
a) 7400
b) 7300
c) 7500
d) 7600
e) 7250
15. Three types of coffee brands A, B and C costs Rs. 85/kg, 100/kg and 50/kg respectively. How many kg of each should be blended to produce 100 kg of mixture worth Rs.80/kg, given that the quantities of B and C are equal?
a) 50, 25, 25
b) 40, 20, 20
c) 35, 15,15
d) 30, 20, 20
e) 45, 10, 10
Solutions:
1. C) Let A can do work in x days, then, B can do same work in 4x days
ATQ, (10/x)+ [(10 + 2)/4x] = 3/4 => (40 + 12)/4x = 3/4 => 3x = 52 => x = 52/3
So, A will alone complete the work in 17 1/3 days
2. A) Let speed of A and B is 2x kmph and 3x kmph respectively.
ATQ, 3x × 3 – 2x × 2 = 50
=> x = 10
Required Sum = 10 (2 + 3) = 50kmph
3. C) Let age of Sweta 5 years ago = 5x
Let age of Neha 5 years ago = 4x
ATQ,
(5x + 10) + (4x + 10) = (100% + 400%/9) (25 + 20)
=> 9x + 20 = 13/9 × 45 => x = 5
Sum of their present ages = (5 + 4) × 5 + 10 = 45 + 10 = 55 years
4. E) Let total article bought = x
So, no. of articles sold at different profit percent = 2/5x, 3/5x
For articles sold at 20% profit
Profit/SP × 100 = 20 => P/S.P = 1/5
So, CP = 4 and SP = 5
For article sold at 33 1/3% profit
P/SP = 1/3
So, CP = 2 and SP = 3
But CP is same for both
Required ratio = [5 × (2x/5)]/[(3 × 2) × (3x/5)] = 5 : 9
5. C) Total salary of A + B + C = 18000 × 3 = 54000
Total salary of B + C + D = 24000 × 3 = 72000
So, D – A = 6000 × 3 = 18000
Given that D = 3A
Therefore 2A = 18000 => A = 9000
Average of B and C = (54000 – 9000)/2 = 22500
6. D) By the allegation rule,
20                   70
            50
20                   30
Therefore ratio of time = 2 : 3
Therefore ratio of distances = 2 × 20 : 3 × 70 = 4 : 21
7. C) Area of ceiling = Total Cost/Cost of 1 sq unit = 6000/10 = 600
l × b = 3x × 2x = 600 => 6(x^2) = 600 => x = 10
l = 30m and b = 20m
Area of the 4 wall = 1920/4 = 480m^2
Therefore Height = 480/2(30 + 20) = 480/(2 × 50) = 4.8m
8. A) let present age of son = x then father’s age = x + 3x = 4x
After 8 years (4x + 8) = 5/2 (x + 8) => 8x + 16 = 5x + 40 => 3x = 24
Therefore, x = 8
Therefore, required answer = (4x + 16)/(x + 16) = (32 + 16)/(8 + 16) = 48/24 = 2
Hence, 2 times would father be his son’s age.
9. D)

Ankit
Bittu
Chintu
Mechanic
CP
100
120
132
120 + 12 = 132
SP
120
132
120
143
Therefore, loss of Ankit = 143 – 120 = 23
Therefore percentage loss of Ankit = (23 × 100)/100 = 23%
10. B) Milk = 3 × 3/5 = 9/5 lit
Water = 3 × 2/5 = 6/5 lit (in first mixture)
Milk – 4x/9 and water – 5x/9 litres in second mixture
So, 9/5 + 4x/9 = 6/5 + 5x/9 => x/9 = 3/5 => x = 27/5 = 5.4 lit
11. A) Let number = a, b and c
a : b = 2 : 5 and b : c = 3 : 4
so, a : b : c = 6 : 15 : 20
Required difference = 123/41 × 20 – 123/41 × 15 = 3(20 – 15) = 15
12. D) Suppose Radhe joined the business after x months.
So Radhe’s money was invested for (12 – x) months.
(1.5 lakh * 12)/{1 lakh * (12 – x)} = 3/1
=> 18 = 3(12 – x)
=> 3x = 18
=> x = 6 months
13. B) Let the sum be P and annual interest be I.
From the 1st condition, P + 31 = 2365 … (1)
According to the 2nd condition, P + 51 = 2655 … (2)
On solving the equations we get, P = Rs 1930 and I = Rs 145
And rate of interest = 145 x 100/1930 = 7.5% (approx)
14. C) Suppose the turnovers of companies XYZ and ABC are 9m and 8m respectively and their expenditures are 17n and 15n respectively.
So, 9m – 17n = 2500 (i)
And 8m – 15n = 2500 (ii)
9 x (ii) – 8 x (i) => 72m – 135n – 72m + 136n = 22500 – 20000
=> n = 2500
Putting in eqn (I), we get, 9m – 42500 = 2500
=> 9m = 45000
=> m = 5000
Turnover of XYZ is 5000*9= 45000 and expenditure of ABC is 2500*15 = 37500.
The difference is 7500
15. A) Let quantity of b and c are n
Then quantity of a is 100 – 2n
Thus, cost of A = 85(100-2n)
Cost of B= 100n
Cost of C= 50n
The total cost of the mixture is 80×100 Thus.
(85(100 -2n)) + 100n + 50n = 80×100
or, 8500 – 170n + 150n = 8000
or, n = 500/20
or, n = 25
So quantity of B and C is 25 kg each and quantity of A is 50 kg =(100 – 2 X 25) = 50 kg