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Maths Quiz for KVS and NVS Exams 2016

Q1. Anu sold 2 books at Rs. 1.40 each. Her profit on one was 20% and her loss on the other was 20%. Then, she:
(a) made no gain no loss
(b) Gained 20 paise
(c) Lost 20 paise
(d) lost 12 paise
Sol.
S.P of 2 books = Rs. 2.80
Over all percentage change
= 20 + (-20) + (20 × (-20))/100=-4 = 4% loss
∴ C.P. = (2.80 × 100)/(100 – 4) = 2.92
⇒ Loss = Rs. 0.12

Q2. A house worth Rs. 150000 is sold by X at 5% profit to Y. Y sells the house back to X at a 2% loss. Then, in the entire transaction:
(a) X gains Rs. 4350
(b) X loses Rs. 4350
(c) X gains Rs. 3150
(d) X loses Rs. 3150
Sol.
X’s gain = (5-2-(5 × 2)/100)% of 1,50,000
= Rs. 4350.

Q3. A businessman marks his goods in such a way that even after allowing 12.5% discount on cash purchase, he gains 20%. If the cost price of the goods is Rs. 140, the marked price is:
(a) Rs. 162
(b) Rs. 172
(c) Rs. 192
(d) Rs. 198
Sol.
Suppose marked price = Rs. K
∴ K – 12.5% of K = 140 + 20% of 140
⇒ 87.5% of K = 140 + 28 = 168
∴ K = 16800/87.50 = 192.

Q4. 6 men can complete a piece of work in 12 days. 8 women can complete the same price of work in 18 days, whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 day how many men would be required?
(a) 36
(b) 24
(c) 18
(d) Cannot be determined
Sol.
Males : Females : Children
6 × 12 : 8 × 18 : 18 × 10
72 : 144 : 180
2 : 4 : 5
So, 2 Males = 4 Females = 5 Children
4 Males + 12 Females + 20 Children
= 4 + 6 + 8 = 18 Males
∵ 6 males finished a piece of work in 12 days.
∴ 18 males finished the work = (12 × 6)/18 = 4 days
Work in 2 days = 2/4=1/2
Rest of the work will be finished in a day by
= 18 × 2 = 36 males

Q5. 2 men alone or three women alone 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
Sol.
2M = 3W
∴ 1M = 3/2W
∴ 1M + 1W = 3/2W + 1W = 5/2W
Number of days = (3 × 4)/(5/2 )=24/5 days

Q6. Ram sets out to cycle from Delhi to Mathura and at the same time Suresh starts from Mathura to Delhi. After passing each other, they complete their journeys in 9 and 16 hours, respectively. At what speed does Suresh cycle if Ram cycles at 16 km per hour?
(a) 12 km/h
(b) 16 km/h
(c) 14 km/h
(d) None of these
Sol.
(Ram^’ s speed)/(Suresh^’ s speed)=√(T_2 )/√(T_1 )=√16/√9=4/3.
∴ Suresh’s speed = 3/4 Ram’s speed
=3/4×16 = 12 km/h.

Q7. A train 300 metres long is running at a speed of 90 km/h. How many seconds will it take cross a 200 metres long train running in the same  direction at a speed of 60 km/h?
(a) 70 seconds
(b) 60 seconds
(c) 50 seconds
(d) None of these
Sol.
Here, L1 = 300 m, L2 = 200 m,
s1 = 90 km/h and s2 = 60 km/h
∴ s1-s2 = 90 – 60 = 30 km/h = 30 × 5/18 m/s
∴ Time taken = (L1+ L2)/(s1- s2 )=(300 + 200)/(30 × 5/18)
= (500 × 18)/(30 × 5) = 60 seconds.

Q8. A person covers half of his journey at 30 km/h and the remaining half at 20 km/h. The average speed for the whole journey is:
(a) 25 km/h
(b) 28 km/h
(c) 32 km/h
(d) None of these
Sol.
Here s1 = 30 and s2 = 20.
∴ Average speed = (2s1 s2)/(s1  + s2 )
= (2 × 30 × 20)/(30 + 20) = 24 km/h.

Q9. Two trains, one 160 m and other 140 m long, are running in opposite directions on parallel rails. The first train at 77 km/h and the other train at 67 km/h. How long will they take to cross each other.
(a) 7 seconds
(b) 7.5 seconds
(c) 6 seconds
(d) 10 seconds
Sol.
Required time = (160 + 140)/((77 + 67)× 5/18)=(300 × 18)/(144 × 5)
= 7.5 seconds.
Q10. A car driver leaves Bangalore at 8:30 am and expects to reach a place 300 km from Bangalore at 12:30 pm. At 10:30 he finds that he has covered only 40% of the distance. By how much % he has to increase the speed of the car in order to keep up his schedule?
(a) 45
(b) 40
(c) 35
(d) 50
Sol.
Distance covered by the car in 2 hours
= (300 × 40)/100 = 120 km
Remaining distance = (300 – 120) = 180 km
Remaining time = (4 – 2) = 2 hours
∴ Required speed = (180/2) = 90 km/h
Increase in the  speed of car = ((90-60)/60) = 50% Join India's largest learning destination

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