Maths Quiz for KVS and NVS Exam 2016

1. Two pipes A and B can fill a tank independently in 10 hours and 15 hours respectively, while pipe C can empty it in 30 hours. All pipes are kept open for 6 hours after which pipes B and C are closed. In what time now onwards would the tank get full?
(a) 6 hours                                    
(b) 2 hours      
(c) 2.5 hours                                 
(d) 3 hours   
Let the capacity of the tank be 30 litres.
So Pipe A can fill 3 litre/hour, Pipe B can fill 2 litre/hour and Pipe C can empty 1 litre/hour.
Together they can fill = 3 + 2 – 1 = 4 litre/hour
Tank filled in 6 hours = 24 litres
Time to fill the remaining tank by pipe A alone = 6/3 = 2 hours

2.Two men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required?
(a) 4                                  
(b) 8                
(c) 6                                  
(d) 2 
2 M x 6 = 2 W x 9 = 3 C x 8
2 M = 3 W = 4 C
The ratio of efficiency of man, woman and children = 1/2: 1/3: 1/4 = 6: 4: 3
Let the work done by a man, a woman and a children in one day be 6 units, 4 units and 3 units respectively.
So the total work to be done = 2x6x6 = 72 units
Work done by 3 women and 4 children in one day = 3 x 4 + 4x 3 = 24 units
Remaining work = 72 – 24 = 48 units
Number of men required to complete the remaining work in one day = 48/6 = 8

3. In a school, there are 3600 students. The ratio of boys to girls is 4 : 5. If twenty percent of the boys and sixty percent of the girls like to play hockey, then how many students do not like to play hockey?
(a) 1520                             
(b) 1250                      
(c) 2008                             
(d) None of these
Total Students in school = 3600
Number of boys = 4/9 x 3600 = 1600
Number of boys who like hockey = 20% of 1600 = 320
Number of girls = 2000
Number of girls who like hockey = 60% of 2000 = 1200
Number of students who do not like hockey = (1600 – 320) + (2000 – 1200) = 2080

4. 42 binders can bind 2800 books in 30 days. How many binders will be required to bind 1600 books in 20 days?
(a) 18
(b) 36
(c) 32
(d) 24
M1D1/W1 = M2D2/W2
=(42*30)/2800 = (x*20)/1600
x = 36 days

5.Two men or three women can complete a piece of work in 4 days. In how many days can 1 woman and 1 man together complete the same piece of work?
(a) 6 days
(b) 24/5 days
(c) 12/1.75 days
(d) Cannot be determined
2 men = 3 women => 1 man + 1 woman = (3/2 +1)women
w1D1 = w2D2 => 3*4 = 5/2*D2 => D2= 24/5 days.

6.A, B, C and D purchase a gift worth Rs. 60/-. A pays 1/3 of what others are paying, B pays 1/3rd of what others are paying and C pays 1/4th of what others are paying. What is the amount paid by D ? 
(a) 15
(b) 16
(c) 18
(d) 14
3A = B + C + D
4A = A + B + C + D, A = 60/4 = 15
3B = A + C + D
4B = A + B + C + D, B = 60/4 = 15
4C = A + C + D
5C = A + B + C + D, C = 60/5 = 12
D = 60 – (15 + 15 + 12) = 60-32=18

7. Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(a) Rs. 15
(b) Rs. 15.70
(c) Rs. 19.70
(d) Rs. 20
Let the amount taxable purchases be Rs. x.
Then, 6% of x=30/100
x=30/100*100/6
x=5
Cost of tax free items = Rs. [25 – (5 + 0.30)]=Rs.19.70

8. Vishal spent 25% of his monthly salary on food, 20% of remaining amount on house rent, and 8% of remaining amount on cloths. Now he is with Rs. 6624. How much amount he spent on cloths?
(a) Rs 884
(b) Rs 778
(c) Rs 712
(d) Rs 576
Let his salary be x
x * 75/100 * 80/100 * 92/100 = 6624
x = 12000
Amount on clothes = 12000 * 80/100 * 75/100 * 8/100 = Rs. 576

9.The population of a city increases by 4% per year but due to migration it decreases by 1% per years. What will be the percentage increase in population in 3 years?
(a) 9%
(b) 9.27%
(c) 27%
(d) 12%
Actual increase in population=3%
Let, earlier population=100 then the population after 3 years
=100(1+3/100)^3=109.2727
∴Required percentage=9.27%

10.The ratio of the present ages of Ram and Rahim is 3 : 2. The ratio of the present ages of Rahim and Aman is 5 : 2. What is the ratio of the present ages of Ram and Aman?
(a) 4 : 15
(b) 15 : 4
(c)  9 : 5
(d) Cannot be determined
(Age of Ram)/(Age of Rahim)=3×5/2×5=15/10
(Age of Rahim)/(Age of Aman)=5/2=10/4; 
∴(Age of Ram)/(Age of Aman)=15/4=15∶4