Maths Quiz for KVS/NVS Exam 2016

Q1. a : b = 4 : 9 if 4 is added to both of the numbers then the new ratio becomes 21 : 46. What is the difference between a and b?
(a) 80
(b) 100
(c) 125
(d) 130
Sol. 
a/b=4x/9x and (a+4)/(b+4)=21/46
a=80 and b=180
∴b-a=100

Q2.. 6 pumps of Kirlosker can fill a tank in 7 days and 2 similar pumps of USHA can fill the same tank in 18 days. What is the ratio of the efficiency of a Kirlosker pump and a USHA pump?
(a) 6 : 7
(b) 7 : 6
(c) 7 : 54
(d) can’t be determined
Sol. 
The number of days required by a single Kirlosker pumps to fill the tank=6×7=42 days and the number of days required by a single USHA pump to fill the same tanks=2×18=36 days.
Now, since efficiency is inversely proportional to the number of days. Hence,
(Efficiency of on K-pump)/(Efficiency of U-pump)=36/42=6/7

Q3. 16 person can reap 1/5th field in 6 days. How many person (with same efficiency) are required to reap rest of the field in 8 days?
(a) 27
(b) 54
(c) 48
(d) 64
Sol.  
1/5th field can be reaped by 96 man days
∴4/5th field can be reaped by 96×4=384 man days
Now, since there are only 8 days so required number of men=384/8=48  men

Q4. Six men earn as much as seven women, two women earn as much as three boys, four boys earn as much as five girls. If a girl earns Rs.16 a week, what does a man earn per week?
(a) Rs.35  
(b) Rs.20
(c) Rs.40  
(d) Rs.30
Sol. 
6 men = 7 women;
2 women = 3 boys;
4 boys = 5 girls;
Now earning of a girls per week = Rs. 16
so Earning of 1 boy = 5/4*16 = 20
Earning of 1 women = 3/2*20 = 30
Earning of 1 man = 7/6*30 = 35

Q5. Find the arithmetic mean of 8 no.between 1 and 10.
(a) 2.5  
(b) 5.5
(c) 3.5  
(d) 4.5
Sol. 
8 arithmetic mean between 1 and 10
= 2,3,4,5,6,7,8,9
Their mean = (2+3+4+5+6+7+8+9)/8 = 5.5

Q6. I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. Then my age and my son’s age are respectively:-
(a) 42 yrs, 14 yrs 
(b) 45 yrs, 15 yrs
(c)36 yrs, 12 yrs 
(d) 48 yrs, 16 yrs
Sol. 
Let the present age of my son = x yrs.
Then,the present age of mine = 3x yrs.
(3x+5)=5/2(x+5)
x = 15 yrs.
Father’s age = 45 yrs.
Son’s age = 15 yrs.

Q7. A money lender finds that due to a fall in the annual rate of interest from 8% to 7(3/4)%, his yearly income diminishes by Rs. 61.50. His capital is
(a) Rs. 22400                          
(b) Rs. 23800
(c) Rs. 24600                          
(d) Rs. 26000
Sol. 
Decrease in rate of interest = 8% – 7 ¾ %
= 8% – 31/4% = ¼ %
Now, ATQ,
¼% of capital = Rs. 61.50
⇒ Total capital (i.e. 100%) = Rs. 61.50 × 4 × 100 = Rs. 24600

Q8. The average age of 40 students of a class is 15 years. When 10 new students are admitted, the average age is increased by 0.2 years. The average age of new students is
(a) 15.2 years                          
(b) 16 years
(c) 16.2 years                          
(d) 16.4 years
Sol.  
Total ages of 40 students = 40 × 15 = 600 years
Let the average age of 10 new students = x yr
(600 + 10x)/50 = 15.2
600 + 10x = 15.2 × 50
600 + 10x = 760
x = (760 – 600)/10
x = 160/10 = 16 yrs.

Q9. A man travels a distance of 24 km at 6 km/hr another distance of 24 km at 8 km/hr and a third distance of 24 km at 12 km/hr. His average speed for whole journey (in km/hr) is
(a) 8(2/3)                             
(b) 8
(c) 2(10/13)                           
(d) 9
Sol. 
T1 = 24/6 = 4 hrs, T2 = 24/8 = 3 hrs,
T3= 24/12 = 2 hrs
Average speed = (24 + 24 + 24)/(4 + 3 + 2) = 72/9 = 8 km/hr

Q10.HCF and LCM of two numbers are 7 and 140 respectively. If the numbers are between 20 and 45, the sum of the numbers,is
(a) 70                                 
(b) 77
(c) 63                                 
(d) 56
Sol. 
H.C.F. × L.C.M. = 7 × 140 = 980
= 1st no. × 2nd no. (between 20 & 45)
= 28 × 35
So, sum of the number = 28 + 35 = 63