Quant Quiz

Problems on Age - Solved Examples(Set 2)

6. The sum of ages of $5$ children born at the intervals of $3$ years each is $50$ years. Find out the age of the youngest child?
A. $6$ years	B. $5$ years
C. $4$ years	D. $3$ years

answer with explanation

Answer: Option C
Explanation:
Let the age of the youngest child $=x$

Then, the ages of $5$ children can be written as $x,(x+3),(x+6),(x+9)$ and $(x+12)$

$x+(x+3)+(x+6)+(x+9)$ $+(x+12)=50$
$\Rightarrow 5x+30=50\Rightarrow 5x=20\Rightarrow x=\frac{20}{5}=4$

7. A is two years older than B who is twice as old as C. The total of the ages of A, B and C is$27$. How old is B?
A. $10$	B. $9$
C. $8$	D. $7$

answer with explanation

Answer: Option A
Explanation:
Let age of C $=x$. Then,
Age of B $=2x$
Age of A $=2+2x$

Total age of A,B and C $=27$
$\Rightarrow (2+2x)+2x+x=27\Rightarrow 5x=25\Rightarrow x=\frac{25}{5}=5$

B's age $=2x=2\times 5=10$

8. The average age of a class of $22$ students is $21$ years. The average increased by $1$ when the teacher's age also included. What is the age of the teacher?
A. $48$	B. $45$
C. $43$	D. $44$

answer with explanation

Answer: Option D
Explanation:
Solution 1

Total age of all students $=22\times 21$

Total age of all students + Age of the teacher $=23\times 22$

Age of the teacher
$=23\times 22-22\times 21=22(23-21)=22\times 2=44$

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Solution 2

If age of the teacher was $21$, average would not have changed.

Since average increased by $1$,
Age of the teacher $=21+23\times 1=44$

9. A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is $38$ years now, what was the son's age five years back?
A. $20$ years	B. $18$ years
C. $14$ years	D. $22$ years

answer with explanation

Answer: Option C
Explanation:
Let son's present age be $x$ years. Then,

$(38-x)=x\Rightarrow 2x=38\Rightarrow x=\frac{38}{2}=19$

Son's age $5$ years back =$19-5=14$

10. Ayisha's age is $1/6\text{th}$ of her father's age. Ayisha's father's age will be twice Shankar's age after $10$ years. If Shankar's eight birthdays was celebrated two years before, then what is Ayisha's present age.
A. $10$ years	B. $12$ years
C. $8$ years	D. $5$ years

answer with explanation

Answer: Option D
Explanation:
Solution 1

Let Ayisha's present age $=x$
Then, her father's age $=6x$

Given that Ayisha's father's age will be twice Shankar's age after $10$ years.
Therefore, Shankar's age after $10$ years $=\frac{1}{2}(6x+10)=3x+5$

Also given that Shankar's eight birthdays was celebrated two years before.
Therefore, Shankar's age after $10$ years $=8+12=20$

$3x+5=20\Rightarrow x=\frac{15}{3}=5$

Therefore, Ayisha's present age $=5$ years

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Solution 2

Shankar's present age $=8+2=10$

Ayisha's father's age after $10$ years $=2(10+10)=40$
Ayisha's father's present age $=40-10=30$

Ayisha's present age $=\frac{1}{6}\times 30=5$

Quant Quiz

Quant Quiz

1. The average of 3 prime numbers lying between 47 and 74 is 191/3.  The greatest possible difference between any two out of the 3 prime numbers is:

(a) 12

(b) 14

(c) 18

(d) 24

(e) can’t be determined

2. The average score of Dhoni after 48 innings is 48 and in the 49th innings Dhoni scores 97 runs. In the 50th innings the minimum number of runs required to increase his average score by 2 than it was before the 50th innings:

(a) 99

(b) 149

(c) 151

(d) 171

(e) can’t be determined

3. In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction, increased by 1. The value of n is:

(a) 21

(b) 20

(c) 22

(d) 24

(e) none of these

4. Bhupesh sells two types of tea viz. Desi Chai and Videshi chai. He sells Desi Chai at Rs. 18 per kg and incurs a loss of 10% whereas on selling the Videshi Chai at Rs. 30 per kg, he gains 20%. In what proportion should the Desi Chai and Videshi chai be mixed such that he can gain a profit of 25% by selling the mixture at Rs. 27.5 per kg?

(a) 3 : 2

(b) 2 : 3

(c) 2 : 5

(d) 3 : 5

(e) none of these

5. The diluted wine contains only 8 litres of wine and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing wine. How many litres of mixture shall be replaced with pure wine if there was initially 32 litres of water in the mixture?

(a) 4

(b) 5

(c) 8

(d) 10

(e) none of these

6. A milk man had a mixture of milk in which ratio of milk and water is 5 : 3. He sells 40 litres of milk i.e, mixture then the adds up 15 litres of pure water. Now the ratio of milk and water is 5 : 4. What is the new quantity of mixture?

(a) 72 litres

(b) 270 litres

(c) 135 litres

(d) data insufficient

(e) none of these

7. Rs. 960 were distributed among A, B, C and D in such in way that C and D together gets half of what A and B together gets and C gets one-third amount of B. Also D gets 5/3 times as much as C. What is the amount of A?

(a) Rs. 240

(b)  Rs. 280

(c) Rs. 320

(d) data insufficient

(e) Rs. 4500

8. The cost of packaging of the mangoes is 40% the cost of fresh mangoes themselves. The cost of mangoes increased by 30% but the cost of packaging decreases by 50%, then the percentage change of the cost of packed mangoes, if the cost of packed mangoes is equal to the sum of the cost of fresh mangoes and cost of packaging:

(a) 14.17%

(b) 7.14%

(c) 6.66%

(d) 8.64%

(e) none of these

9. Abhinav scores 80% in Physics and 66% in chemistry and the maximum marks of both the papers are 100. What per cent does he score in Maths which is of 200 marks, if the scores 80% marks in all the three subjects:

(a) 74 %

(b) 84 %

(c) 87 %

(d) 83 %

(e) none of these

10. A dishonest trader marks up his goods by 80% and gives discount of 25%. Besides he gets 20% more amount per kg from wholeseller and sells 10% less per kg to customer. What is the overall profit percentage?

(a) 80 %

(b) 60 %

(c) 70 %

(d) 65 %

(e) none of these

11. A merchant earns 25% profit in general. Once his 25% consignment was abducted forever by some goondas. Trying to compensate his loss he sold the rest amount by increasing his selling price by 20%. What is the new percentage profit or loss?

(a) 10 % loss

(b) 12.5 % loss

(c) 12.5 %    profit

(d) 11.11% loss

(e) none of these

12. Akbar lends twice the interest received from Birbal to chanakya at the half of the interest at which he lent to Birbal. If Akbar lent Rs. P @ r% per annum for 1 year to Birbal then the interest received by Akbar from Chanakya is:

(a) Pr2/100

(b) (Pr/10)2

(c) P (r/10)2

(d) P (r/100)2

(e) none of these

13. The ratio of the amount for two years under CI annually and for one year under SI is 6 : 5. When the rate of interest is same, then the value of rate of interest is:

(a) 12.5 %

(b) 18 %

(c) 20 %

(d) 16.66 %

(e) none of these

14. Sunidhi borrowed Rs. 10815, which is to be paid back in 3 equal half yearly installments. If the interest is compounded half yearly at 40/3% per annum, how much is each installment?

(a) 2048

(b) 3150

(c) 4096

(d) 5052

(e) none of these

15. The difference between simple and compound interest for the fourth year is Rs. 7280 at 20% p.a. What is the principal sum?

(a) 10000

(b) 5000

(c) 1 lakh

(d) 4000

(e) 8275

Answers...

Quant Quiz

Quant Quiz

1. A, B, C enter into a partnership with shares in the ratio (7/2) : (4/3) : (6/5). After 4 months,

 A increase his share by 50%. If the total profit at the end of one year be Rs. 21600, then B’s share in the profit is

(a) Rs. 2100

(b) Rs. 2400

(c) Rs. 3600

(d) Rs. 4000

(e) None of these

2. A, B and C invested capitals in the ratio 3 : 5 : 9; the timing of their investments being in the ratio 2 : 3 : 1. 

In what ratio would their profits be distributed?

(a) 2 : 5 : 3

(b) 3 : 2 : 5

(c) 7 : 5 : 3

(d) 9 : 7 : 11

(e) None of these 

3. What  value of ‘k’ , must be added to 7, 16, 43, 79  so that they will be in proportion

(a) 7

(b) 5

(c) 9

(d) 11

(e) None of these

4. The incomes of A and B are in the ratio 3 : 2 and their expenditures in the ratio 5 : 3. 

if each saves Rs. 1000, A’s income is

(a) Rs. 5000

(b) Rs. 6000

(c) Rs. 8000

(d) Rs. 7000

(e) None of these

5. The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was Rs. 22.

 Find the amount of the bill.

(a) Rs. 3200

(b) Rs. 2200

(c) Rs. 1800

(d) Rs. 2800

(e) None of these

6. If the given two numbers are respectively 7% and 28% of a third number,

 then what percentage is the first of the second?

(a) 20%

(b) 25%

(c) 18%

(d) 14%

(e) None of these

7. To find out the total compound interest accrued on a sum of money after 5 years, 

which of the following information’s given in the statements P and Q will be sufficient?

P : The sum was  Rs. 20000.

Q : The total amount of simple interest on the sum after 5 years was Rs. 4000.

(a) Only P is sufficient

(b) Only Q is sufficient

(c) Either P or Q is sufficient

(d) Both P & Q are needed

(e) Both P and Q are not sufficient.  

8. A sum of Rs. 10 is lent to be returned in 11 monthly installments of Rs. 1 each, interest being simple. The rate of interest is :

(a) 9 1/11 %

(b) 10%

(c) 11%

(d) 21 9/11%

(e) 8 ¾%

9. A can do a piece of work in 10 days, while B alone can do it in 15 days. 

They work together for 5 days and the rest of the work is done by C in 2 days.If they get Rs. 450 for the whole work, how should they divide the money?

(a) Rs. 250, Rs. 100, Rs. 100

(b) Rs. 220, Rs. 150, Rs. 75

(c) Rs. 200, Rs. 150, Rs. 100

(d) Rs. 175, Rs. 175, Rs. 100

(e) None of these

10. A can do a piece of work in 30 days, B in 50 days and C in 40 days. If A is assisted by B on one day and by C on the next day-

 alternately then work will be completed in -

(a)    17 32/35 days

(b)   12 2/3 days

(c)    16 31/37 days

(d)   18 1/3 days

(e)    None of these

Answers...