Maths Quiz for KVS and NVS Exams 2016

Q1.Three students A, B and C play cricket. The runs scored by A and B respectively are in the ratio 3 : 2. B’s runs to C’s runs are also in the same ratio. Together they score 342 runs. Then the runs scored by B are
(1) 216
(2) 108
(3) 90  
(4) 171
Sol. 
A : B  = 3 : 2 = 9 : 6
B : C = 3 : 2 = 6 : 4
so A : B : C = 9 : 6 : 4
so Runs scored by B = 6/19 * 342
= 108

Q2.A father is 7 years older than the mother and the mother’s age now is 3 times the age of the daughter. The daughter is 10 years old now. What was the father’s age when the daughter was born?
(1) 27 years
(2) 37 years
(3) 15 years
(4) 40 years
Sol.
 Mother’s present age
= 30 years
Father’s present age = 37 year
Father’s age 10 years ago
= 37 – 10 = 27 years

Q3.Of the three numbers, the first is twice the second and is half of the third. If the average of these numbers is 56, the numbers in order are.
(1) 96, 24, 48
(2) 96, 48, 24
(3) 48, 96, 24
(4) 48, 24, 96
Sol. 
Second number = x (let)
First number = 2x
Third number = 4x
so x  + 2x + 4x = 56 * 3
=> 7x = 56 * 3
x = 8 * 3 = 24
Other numbers are : 48 and 96

Q4. From a vessel containing 100L of wine, 10L are drawn out and an equal amount of water is added. From the mixture, 10L is again drawn out and same quantity of water is added.What is the final ratio of wine to water?
(1) 90:10
(2) 91:9
(3) 81:19
(4) 80:20
Sol.
 Here, a=10L, n=2 and x=100L
Quantitiy of wine in end =x(1-a/x)^n
=100(1-10/100)^2
=81L
Required ratio =81:(100-81)=81:19

Q5. The marks of 3 students A,B and C are in the ratio of 10:12:15.If the maximum marks of the paper are 100,then the marks of B cannot be in the range of
(1) .40-50
(2) 70-50
(3) 70-60
(4) 80-90
Sol.
 Let the marks of A,B and C are 10x,12x and 15X respectively.
 maximum marks of C=15*6=90 and maximum marks of
 b=12*6=72 hence the marks of B cannot be in the range of (80-90)

Q6. Mukesh uses 920 g in place of 1 kg to sell his goods.When he sells his article at 15% gain on the cost price,the actual percentage of profit is
(1) 21
(2) 25
(3) 9  
(4) 17
Sol.
Let CP=Rs 1000
Actual CP=Rs 920 and selling price =(1000*115)/100 = 1150
Actual profit percentage = (1150-920)/920 * 100% =25%

Q7.When a dealer heard that the price of certain product was about to increase Rs. 5 per pack, he purchased a number of packs of this product for Rs. 4,500/-. Had he purchased it at the new price, he would have obtained 10 fewer packs. How many packs did he buy’?
(1) 90  
(2) 100
(3) 50  
(4) 125
Sol.
 Let the number of purchased pack = x
so According to question.
4500/x = 4500/x -10 – 5
or, 4500 [1/(x )-1/(x – 10)] = -5
or, 900 [1/(x – 10)  – 1/(x )] = 1
or, (900 [x – (x – 10) ])/((x – 10)x)= 1
or, 900 * 10 = x^2 – 10x
or , x^2 – 10x – 9000 = 0
or x^2 – 100x + 90x – 9000
= 0
or, x(x – 100) + 90 (x -100)
= 0
or, (x + 90) (x – 100) = 0
or, x = – 90 and 100
Since the value of x should not be negative, therefore, the required answer is 100.

Q8.How many kilograms of coffee price at Rs. 33 per kg should be mixed with the coffee at Rs. 27 per kg so that the 60 kg of mixture costs Rs. 32 per kg?
(1) 30  
(2) 20
(3) 50  
(4) 10
Sol.
By using allegation method,
We get the ratio of kg of coffee of 33 kg price to the 27 kg price=5:1
So 50 kg of coffee is mixed with 10 kg of coffee to get the price of 32 per kg of coffee for amount of 60 kg

Q9.If A and B work together, they complete a work in 3 days, B  and C together complete the same work in 6 days, while A and C complete that work in 8 days.  all of them will  complete the work in how many days? Choose the most appropriate option
(1) More than 3 days
(2) More than 2 days
(3) Less than 3 days
(4) More than 4 days
Sol. 
work done by 2(A + B + C) in one day
= (1/3  +1/6+1/8 )
= (8 + 4 + 3)/24 = 15/24 = 5/8 part
so (A + B + C)’s one day work
= 5/8*2 = 5/16 work
so Whole work can be done by
(A + B + C) in 16/5 days
Therefore, the required answer is option (1).

Q10. A boat covers a distance of 30 km downstream in 2 hours while it takes 6 hours to cover the same distance upstream.If the speed of current is half of the speed of the boat then, what is the speed of boat in km per hour?
(1)15 kmph
(2) 5 kmph
(3) 10 kmph
(4) Data inadequate.
Sol.
Downstream speed = 30/2 =15 km/h
Upstreams speed = 30/6 = 5 km/h
so speed of the boat = 1/2(15+5)
=1/2 x 20 = 10 km/h