Quant Quiz

Problems on Age - Solved Examples(Set 1)

1. Ten years ago, P was half of Q's age. If the ratio of their present ages is $3:4$, what will be the total of their present ages?
A. $45$	B. $40$
C. $35$	D. $30$

answer with explanation

Answer: Option C
Explanation:
Let present age of P and Q be $3x$ and $4x$ respectively.

Ten years ago, P was half of Q's age
$\Rightarrow (3x-10)=\frac{1}{2}(4x-10)\Rightarrow 6x-20=4x-10\Rightarrow 2x=10\Rightarrow x=5$

Total of their present ages
$=3x+4x=7x=7\times 5=35$

2. Father is aged three times more than his son Sunil. After $8$ years, he would be two and a half times of Sunil's age. After further $8$ years, how many times would he be of Sunil's age?
A. $4$ times	B. $5$ times
C. $2$ times	D. $3$ times

answer with explanation

Answer: Option C
Explanation:
Assume that Sunil's present age $=x$.
Then, father's present age $=3x+x=4x$

After $8$ years, father's age $=2\frac{1}{2}$ times of Sunils' age
$\Rightarrow (4x+8)=2\frac{1}{2}(x+8)\Rightarrow 4x+8=\frac{5}{2}(x+8)\Rightarrow 8x+16=5x+40\Rightarrow 3x=40-16=24\Rightarrow x=\frac{24}{3}=8$

After further $8$ years,
Sunil's age $=x+8+8=8+8+8=24$
Father's age $=4x+8+8=4\times 8+8+8=48$

Father's age/Sunil's age $=\frac{48}{24}=2$

3. A man's age is $125\%$ of what it was $10$ years ago, but $83\frac{1}{3}\%$ of what it will be after $10$years. What is his present age?
A. $70$	B. $60$
C. $50$	D. $40$

answer with explanation

Answer: Option C
Explanation:
Let the age before $10$ years $=x$. Then,

$\frac{125x}{100}=x+10\Rightarrow 125x=100x+1000\Rightarrow x=\frac{1000}{25}=40$

Present age $=x+10=40+10=50$

4. A man is $24$ years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
A. $23$ years	B. $22$ years
C. $21$ years	D. $20$ years

answer with explanation

Answer: Option B
Explanation:
Let present age of the son $=x$ years
Then, present age the man $=(x+24)$ years

Given that, in $2$ years, man's age will be twice the age of his son
$\Rightarrow (x+24)+2=2(x+2)\Rightarrow x=22$

5. Present ages of Kiran and Syam are in the ratio of $5:4$ respectively. Three years hence, the ratio of their ages will become $11:9$ respectively. What is Syam's present age in years?
A. $28$	B. $27$
C. $26$	D. $24$

answer with explanation

Answer: Option D
Explanation:
Ratio of the present age of Kiran and Syam $=5:4$

Let present age of Kiran $=5x$
Present age of Syam $=4x$

After $3$ years, ratio of their ages $=11:9$
$\Rightarrow (5x+3):(4x+3)=11:9\Rightarrow 9(5x+3)=11(4x+3)\Rightarrow 45x+27=44x+33\Rightarrow x=33-27=6$

Syam's present age $=4x=4\times 6=24$

Quant Quiz

Quant Quiz

Directions : Each of the questions below consists of a question and two statements numbered I and II given below it. 

You have to decide whether the data provided in the statements are sufficient to answer the question. 
Read both the statements and Give answer

1) if the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.

2) if the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.

3) if the data either in Statement I alone or in Statement II alone is sufficient to answer the question.

4) if the data in both the Statements I and II even together are not sufficient to answer the question.

5) if the data in both the Statements I and II together are necessary to answer the question.

1. What is the area of a square?

I. The measure of the diagonal of the square is 80 cm.

II. The perimeter of the square is equal to the circumference of a circle.

2. What is Asha’s present salary?

I. Her salary increases every year by 15 per cent.

II. She joined the organisation seven years ago.

3. What is the rate of interest p.c.p.a.?

I. The compound interest accrued on an amount of Rs 1,500 at the end of 2 years is Rs 660.

II. An amount doubles itself in 5 years at simple interest.

4. What is the total staff strength of the organisation?

I. 75% of the staff consists of male employees.

II. The ratio of female to male employees in the organisation is 1 : 3.

5. What is a two-digit number?

I. The sum of the two digits of the number is 8.

II. The number obtained by interchanging the two digits of the number is lesser than the original number by 18.

Directions: Study the table carefully to answer the following questions.

Percentage of marks obtained by six students in six different subjects

6. What is the approximate average marks obtained by all students together in Hindi?

1) 45 

2) 51 

3) 62 

4) 59 

5) 66

7. What is the ratio of the marks obtained by students A, B and C together in Maths to the marks obtained by students D, 
E and F together in Marathi?

1) 7 : 22 

2) 23 : 7 

3) 23 : 4 

4) 4 : 21 

5) None of these

8. Which student has scored the second highest in all the subjects together?

1) D 

2) F 

3) A 

4) B 

5) None of these

9. In order to pass the exam, if the students need minimum 75 marks in Social Studies and minimum 85 marks in Science, 

how many students have passed the exam?

1) None 

2) One 

3) Two 

4) Three 

5) None of these

10. What is the percentage of marks obtained by B in all the subjects together? (rounded off to two digits after decimal)

1) 68.62 

2) 66.83 

3) 69.24 

4) 64.84 

5) None of these

Answers

1. 1

I alone is sufficient because area of a square

= [diagonal of square/ sqroot(2)]^2

Since we have information regarding the diagonal of the square, it is easy to get the square.

 II alone is not sufficient because the circumference of the circle is not known.

2. 4; We need some more information, such as the salary she was getting seven years ago.

3. 3;

Form I: We have 1500 (1 + r/100)^2 = 1500 + 660

Where r = rate of interest per annum)

1 + r/100 = sqroot(2160/1500)

1 + r/100 = 1 + 20/100

r = 20%

From II: Rate of interest per annum = 100/2 = 20%

4. 4

Neither of the two informations give clues regarding absolute number of employees.

5. 5

Suppose the two-digit number is 10x + y.

Now,

From I: We have x + y = 8

From II: We have x - y = 2

Now,

From I and II: we get

x = 5 and y = 3

Hence, the number is 53 (because 53 > 35)

6. 2

Required average = (65 + 75 + 60 + 70 + 55 + 60)/6 = 385/6 = 64 1/6

Aprox average marks = 64 1/6% of 80 = 51 approx

7. 5

= [150 * (84 + 70 + 66)%]/{50 * (60 + 74 + 76)] = (150 * 220)/(50 * 210)

8. 2

109. 3; Look at the chart given in the answer to the last question.

It is obvious that among the six students only A and C have passed the exam according to the given condition.

10. 1; The required per cent marks = 446/650 * 100 = 68.62%

Quant Quiz

Quant Quiz

1. The price of shirts at Sahara Ganj is defined as Rs. (100 + 10x²) where x is the number of shirts. 

Mallika purchased 5 shirts from the above shop. The average price of a shirt is :

(a) Rs. 70

(b) Rs. 50

(c) Rs. 75

(d) Rs. 85

(e) none of these

2. There are 10 compartments in passenger train which carries on an average 20 passengers per compartment. 

If at least 12 passengers were sitting in each compartment and no any compartment has equal number of passengers-

 then maximum how many passengers can be accommodated in any compartment:

(a) 64

(b) 45

(c) 56

(d) 65

(e) none of these

3. There are twice the number of two wheelers as there are three wheelers and the number of 4 wheelers are equal to the number
 of two wheelers. The average number of wheel per vehicle is :

(a) 3

(b) 4

(c) 5

(d) 7

(e) none of these

4. In a mixture of milk and water, there is only 26% water. After replacing the mixture with 7 litres of pure milk,

 the percentage of milk in the mixture become 76%. The quantity of mixture is : 

(a) 65 litre

(b) 91 litre

(c) 38 litre

(d) 87 litre

(e) none of these

5. The ratio of expenditure and savings is 3 : 2. If the income increases by 15% and the savings increases by 6%, 

then by how much per cent should his expenditure increases?

(a) 25

(b) 21

(c) 12

(d) 24

(e) 54

6. The ratio of petrol and kerosene in the container 3 : 2. when 10 litres of the mixture is taken out and is replaced by the kerosene, 
the ratio becomes 2:3. The total quantity of the mixture in the container is :

(a) 25

(b) 30

(c) 45

(d) 96

(e) none of these

7. Two liquids are mixed in the ratio 4 : 3 and the mixture is sold at Rs. 20 with a profit of 33 1/3%. 

If the first liquid is costlier than the second by Rs. 7. Find the sum of the costs of both the liquids:

(a) Rs. 11

(b) Rs. 29

(c) Rs. 35

(d) Rs. 70

(e) Rs. 125

8. Alloy A contains 40% gold and 60% silver. Alloy B contains 35% gold and 40% silver and 25% copper. 

Alloys A and B are mixed in the ratio of 1 : 4. What is the ratio of gold and silver in the newly formed alloy is?

(a) 20% and 30%

(b) 36@ and 44%

(c) 25% and 35%

(d) 49% and 36%

(e) 64% and 25%

9. Mitthu Bhai sells rasgulla (a famous sweets) at Rs. 15 per kg. A rasgulla is made up of flour and sugar in the ratio of 5 : 3. 

The ratio of price of sugar and flour is 7 : 3 (per kg). Thus he earns

66 2/3% profit. What is t he cost price of sugar?

(a) Rs. 10/kg

(b) Rs. 9/kg

(c) Rs. 18/kg

(d) Rs. 14/kg

(e) Rs. 21/kg

10. In an office there were initially n employees. The HR manager first hired P% employees then after a month q% employees left the office, 

then there were finally n employees remained in the office, the value of p-q is.

(a) pq

(b) pq/100

(c) p/q

(d) p²q/n

(e) none of these 

11. The pressure of a definite mass of a gas is directly proportional to the temperature and inversely proportional to-
 the volume under the given conditions. If temperature is increased by 40% and the volume is decreased by 20% then the new pressure will:

(a) be increased by 75%

(b) reduce to 25%

(c) be increased by 20%

(d) increase by 28%

(e) None of these

12. A computer typist types a page with 20 lines in 10 minutes but he leaves 8% margin on the left side of the page. 

Now he has to type 23 pages with 40 line on each page which he leaves 25% more margin than before. 
How much time is now required to type these 23 pages.

(a) 7 ½ hrs

(b) 7 2/3 hrs

(c) 23 ½ hrs

(d) 3.916 hrs

(e) None of these

13. Eklavya can do the 6 times the actual work in 36 days while Faizal can do the one fourth of the original work in 3 days. 

In how many days will both working together complete the 3 times of the original work?

(a) 6

(b) 10

(c) 12

(d) 15

(e) none of these

14. A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. 

The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, 

the group would have finished the job in 55% of the time. How many workers were there in the group?

(a) 50

(b) 40

(c) 45

(d) 10

(e) none of these

15. A group of men decided to d a job in 4 days. But since 20 men dropped out every day, the job completed at the end of the 7th day. 

How many men were there at the beginning?

(a) 240

(b) 140

(c) 280

(d) 150

(e) none of these

Answers..

6.Given ratio of petrol and kerosene

Petrol : Kerosene = 3 : 2

After replacement of 10 lt mixture with 10 litre kerosene

Petrol : Kerosene = 2 : 3

For petrol, putting the values, we will get

⇒    Total Quantity = 30 lt.

Quant Quiz

Quant Quiz

1. 1/37 * 5106 + 9/23 * 5681 = ? * 3
1. 518
2. 642
3. 787
4. 896
5. 936


2. cube root(12167) + cube root(4096) = sqroot(?)
1. 1369
2. 1521
3. 1681
4. 1849
5. 2203

3. 17.16 / 0.37 + 24.32 / 0.38 = ?
1. 112
2. 136
3. 13.806
4. 14.208
5. 15.688

4. 0.32% of 1658 + 0.48% of 2145 =?
1. 11.264
2. 12.718
3. 13.806
4. 14.208
5. 15.688

5. 7164 / 59.7 * 7.85 = ?
1. 648
2. 712
3. 884
4. 942
5. 1024

Directions: What will be the next number in the following number series-
6. 3, 8, 34, 206, 1650, ?
1) 16502
2) 17124
3) 17316
4) 18212
5) 18946

7. 4, 10, 18, 28, 40, ?
1) 48
2) 52
3) 54
4) 56
5) 58

8. 7, 61, 211, 505, 991, ?
1) 1512
2) 1587
3) 1643
4) 1717
5) 1751

9. 842, 425, 147, 42.75, ?
1) 12.15
2) 14.95
3) 16.35
4) 18.75
5) 20.25

10. 8.8, 35.2, 76.8, 134.4, 208, ?
1) 297.6
2) 312.4
3) 320.8
4) 324
5) 336.2



Answers

1. 3

2. 2

3. 1

4. 5

5. 4

6. 1; Series is ×2 + 2, ×4 + 2, ×6 + 2

7. 3; Series is + 6, +8, +10, +12 ---------

8. 4; Series is 23 - 1, 43 -3, 63

- 5, 83 - 7

9. 2; Series is + 8 ÷ 2, +16 ÷ 3, +24 ÷4 ------

10. 1; Series is 8 × 1.1, 16 × 2.2, 24 × 3.2, 32 × 4.2