Maths Quiz for KVS and NVS Exam 2016


1. Simmons purchased a refrigerator on the terms that he is required to pay Rs. 1500 cash down payment followed by Rs. 1020 at the end of first year, Rs. 1003 at the end of second year and Rs. 990 at the end of third year. Interest is charged at the rate of 10% per annum compound interest. What is the cash price of the refrigerator?
(a) Rs.  4000                        
(b) Rs. 4100
(c) Rs. 4150                        
(d) Rs. 4200
Cash price of refrigerator = 1500 + 1020/1.1 + (1003)/(1.1)2 + 990/(1.1)3
= 1500 + 1020/1.1 + 1003/1.21 + 990/1.331
= 1500 + 2500
= 4000

2. Alex and Bobin together can complete a work in 12 days. Alex alone can complete in 20 days. If Bobin does the work only half a day daily, then in how many days, Alex and Bobin together will complete the work?
(a) 10 days                          
(b) 20 days
(c) 11 days                          
(d) 15 days
When Bobin works normally then days taken by Bobin to complete the work = (20 × 12)/(20 – 12) days
= 30 days
Now, If Bobin does the work only half a day daily ⇒  Bobin will take twice the total days to complete the whole work alone
⇒ Now No. of days taken by Bobin = (30 × 2) days
= 60 days
So, Now days taken by (Alex + Bobin) together to do the whole work = (20 × 60)/ (20 + 60) = 15 days

3. Anand takes 10 days less than the time taken by Bakshi to finish a piece of work. If both Anand and Bakshi can do it in 12 days, then the time taken by Bakshi alone to finish the work is
(a) 30 days                          
(b) 27 days
(c) 20 days                          
(d) 25 days
Let time taken by Bakshi in completing the work = x day
∴ Time taken by Anand (x – 10) days
∴ 1/x + 1/(x – 10) = 1/12
⇒ (x – 4) (x – 30) = 0
⇒ x = 30 because x ≠ 4

4. A takes 5 days more than B to do a certain job and 9 days more than C; A and B together can do the job in the same time as C. How many days A would take to do it ?
(a) 16 days                          
(b) 10 days
(c) 15 days                          
(d) 20 days
Let days taken by A to do the whole work = x days
So, days taken by B to do the whole work = (x – 5) days
And, days taken by C to do the whole work = (x – 9) days
According to the question
Days taken by (A + B) together to do the whole work = Days taken by C alone to do the whole work
⇒ (x (x – 5))/(x + (x – 5)) = x – 9
or, (x – 3) (x – 15) = 0
⇒ x = 3 or 15
But x = 3 is not possible as x – 5 or x – 9 will become negative.
So, x = 15 days

5. A pipe of diameter d can drain a certain water tank in 40 minutes. The time taken by a pipe of diameter 2d for doing the same job in :
(a) 5 minutes                      
(b) 10 minutes
(c) 20 minutes                    
(d) 80 minutes
Time µ 1/(cross – sectional area of the pipe)
Time µ 1/(π/4 d2)
Time µ 1/d2
So, t2 = t1 (d1/d2)2
t1 = 40 minutes, d1 = d, d2 = 2d
∴ t2 = 40 (d/2d)2
t2 = 40(1/2)2
t2 = 10 minutes
⇒ time taken by a pipe of diameter 2d for doing the same job = 10 minutes

6. Two pipes A and B can fill a water tank in 20 and 24 minutes respectively and a third pipe C can empty at the rate of 3 gallons per minute. If A, B and C opened together fill the tank in 15 minutes, the capacity (in gallons) of the tank is:
(a) 180                                
(b) 150
(c) 120                                
(d) 60
Let the capacity of the tank be x gallons.
Quantity of water filled in the tank in 1 minute when all the pipes A, B and C are opened simultaneously = x/20 + x/24 – 3
According to the question, x/20 + x/24 – 3 = x/15
⇒ x = (3 × 120)/3 = 120 gallons

7. Two  bullets of shot gun were fired at a place at an interval of 28 minutes 30 seconds. A person approaching the firing point in his car hears the two sounds at an interval of 27 minutes. The speed of sound is 330 m/ sec. What is the speed of the car ?
(a) 44 km/hr                      
(b) 66 km/hr
(c) 64 km/hr                      
(d) 54 km/hr
Let speed of car = x km/hr.
Here, Distance covered by the car in 27 minutes = Distance covered by the sound in (28 minutes 30 seconds – 27 minutes)
 ⇒ x km/hr × (27/60) hr.
= (300 × 18/5 km/hr) × (1.5/60 hr)
⇒ x = 66
⇒ Speed of car = 66 km/hr.

8. In a race of 600 metres, Sonu beats Monu by 60 metres and in a race of 500 metres, Monu beats Bablu by 25 metres. By how many metres will Sonu beat Bablu in a 400 metre race ?
(a) 48 m                              
(b) 52 m
(c) 56 m                              
(d) 58 m
In the race between Sonu and Monu.
Distance travelled by Sonu and Monu in same time = 600 mtr. & (600 – 60) mtr = 600 mtr. & 540 mtr.
⇒ In the same time,
Ratio of distance travelled by Sonu & Monu = 10 : 9
Similarly,
In the same time, Ratio of distance travelled by Monu & Bablu = 500 : (500 – 25)
= 500 : 475
= 20 : 19
So, In the same time
Ratio of distance travelled by Sonu, Monu & Bablu = 10 × 20 : 9 × 20 : 9 × 19
= 200 : 180 : 171
⇒ When Sonu travels 200 m, Bablu will travel 171 m
So, When Sonu travels 400 m, Bablu will travel 342 m
⇒ In 400 m race between Sonu & Bablu,
Required No. of metres by which Sonu will win the race = 400 m – 342 m
= 58 m

9. Two trains are running on parallel lines in the same direction at speeds of 40 kmph and 20 kmph respectively. The faster train crosses a man in the second trains in 36 seconds. The length of the faster train is
(a) 200 metres                    
(b) 185 metres
(c) 225 metres                    
(d) 210 metres
Let x = length of the faster train ( in mtr.)
So, 36 seconds = (x + 10)/((40 – 20) kmph)
⇒ x = 36 second × 20 × 5/18  m/sec
= 200 mtr.

10. A boat goes down stream at x km/h and upstream at y km/h. The speed of the boat in still water is
(a) 0.5 (x + y)                      
(b) 0.5 (x – y)
(c) x + y                              
(d) x – y
Speed of boat in still water = (Sdown + Sup)/2
= (x + y)/2 = 0.5 (x + y)