MATHS QUIZ

1. Ayisha’s age is 1/6th of her father’s age. Ayisha ‘s father’s age will be twice the age of 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

A. Insufficient data

B. 16, 30, 40

C. 16, 28 40

D. 16, 28, 36

 3.39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

A. 10

B. 13

C. 14

D. 15

4.Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ?

A. Rs.182.50

B. Rs.170.5

C. Rs.175.50

D. Rs.180

5.If 6 years are subtracted from the present age of Ajay and the remainder is divided by 18, then the present age of Rahul is obtained. If Rahul is 2 years younger to Denis whose age is 5 years, then what is Ajay ‘s present age?

A. 50 years

B. 60 years

C. 55 years

D. 62 years

6.he difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number?

A. 60

B. 80

C. 40

D. 120

 7.The ratio of the age of a man and his wife is 4:3. At the time of marriage the ratio was 5:3 and After 4 years this ratio will become 9:7. How many years ago were they married?

A. 8 years

B. 10 years

C. 11 years

D. 12 years

8.A poultry farm has only chickens and pigs. When the manager of the poultry counted the heads of the stock in the farm, the number totaled up to 200. However, when the number of legs was counted, the number totaled up to 540. How many chickens were there in the farm?

A. 70

B. 120

C. 60

D. 130

9.Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

A. 10

B. 12

C. 14

D. 16

10.A manufacture offers a 10% discount on the market price of a machine and yet makes a profit of 10%. If he gains Rs. 900 per machine, what is the market price of each machine?

A. 9000

B. 12000

C. 10000

D. 11000

ANSWERS AND SOLUTION
1.(D)Explanation :
Consider Ayisha’s present age = x
Then her father’s age = 6x
Given that Ayisha ‘s father’s age will be twice the age of Shankar’s age after 10 years
=> Shankar’s age after 10 years = ½(6x + 10) = 3x + 5
Also given that Shankar’s eight birthdays was celebrated two years before =>Shankar’s age after 10 years = 8 + 12 = 20
=> 3x + 5 = 20
=> x = 15/3 = 5
=> Ayisha ‘s present age = 5 years

 2(D)Explanation :
Let’s take the present age of A,B and C as 4x, 7x and 9x respectively
Then
(4x – 8) + (7x – 8) + (9x – 8) = 56
=> 20x = 80
=> x = 4
Hence the present age of A, B and C are 4×4, 7×4 and 9×4 respectively
ie, 16,28 and 36 respectively.

3(B)Explanation:
Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons     30  : 39
                                      :: 12 : x
Working hours/day 6    :   5

 30 x 6 x x = 39 x 5 x 12
 x = (39 x 5 x 12)/(30 x 6)
 x = 13.

4(C)Explanation :
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed in the ratio 1 : 1
So their average price = (126+135)2=130.5
Hence let’s consider that the mixture is formed by mixing two varieties of tea.
one at Rs. 130.50 per kg and the other at Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. Now let’s find out x.
By the rule of alligation, we can write as
Cost of 1 kg of 1st kind of tea Cost of 1 kg of 2nd kind of tea
                      130.50                       x
                                       Mean Price
                                              153
                   (x – 153)                                              22.50
(x – 153) : 22.5 = 1 : 1
=>x – 153 = 22.50
=> x = 153 + 22.5 = 175.5

5 (B)Explanation :
Present age of Denis = 5 years
Present age of Rahul = 5-2 = 3
Let the present age of Ajay = x
Then (x-6)/18 = present age of Rahul = 3
=> x- 6 = 3×18 = 54
=> x = 54 + 6= 60

 6(B)Explanation
Let the original number be x.
Let A be the value obtained when x is increased by 12.5%.
Therefore, A = x + 12.5% of x
Let B be the value obtained when x is decreased by 25%.
Therefore, B = x – 25% of x
The question states that A – B = 30
i.e., x + 12.5% of x – (x – 25% of x) = 30
x + 12.5% of x – x + 25% of x = 30
37.5% of x = 30
x = 30/37.5*100 = 8

7 (D)Explanation :
Let the present age of the man and his wife be 4x and 3x respectively.
After 4 years this ratio will become 9:7
=> (4x + 4)/ (3x + 4) = 9/7
=> 28x + 28 = 27x + 36
=> x = 8
=> Present age of the man = 4x = 4×8 = 32
Present age of his wife = 3x = 3×8 = 24
Assume that they got married before t years. Then
(32 – t) / (24 – t) = 5/3
=> 96 – 3t = 120 – 5t
=> 2t = 24
=> t = 24/2 = 12

8(D) Explanation
Let there by ‘x’ chickens and ‘y’ pigs.
Therefore, x + y = 200 — (1)
Each chicken has 2 legs and each pig has 4 legs
Therefore, 2x + 4y = 540 — (2)
Solving equations (1) and (2), we get x = 130 and y = 70.
There were 130 chickens and 70 pigs in the farm.

9(C)Explanation:
Part filled in 2 hours = 2/6 = 1/3
Remaining part = (1 – 1/3) = 2/3
 (A + B)’s 7 hour’s work = 2/3
(A + B)’s 1 hour’s work = 2/21
 C’s 1 hour’s work = { (A + B + C)’s 1 hour’s work } – { (A + B)’s 1 hour’s work }
 = (1/6 – 2/21) = 1/14
C alone can fill the tank in 14 hours.

10(D)Explanation :
Let m price = 100
Discount = 10%
so SP = 90
Profit = 10%
Cp= 90×100/110= 900/11
Profit= Sp- Cp , (90-81.81)= 8.19
profit Rs 8.19 then  m price =100
so profit of a machine is Rs. 900 then m price is 11000