 # Maths Quiz for 2016-17 Exams

Q1. A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds. The length of the train (in metres) is:
(a) 188
(b) 176
(c) 175
(d) 96
Let the length of train = L meter
And speed of train = S m/s
L = S × 8
S = L/8 m/s
S = (L + 264)/20
L/8=(L+264)/20
5L/2-L=264
L = 264 ×2/3
L = 176 meter

Q2. A 150 metre long train crosses a 500 metre long bridge in 30 seconds. What time will it take to cross a platform 370 metre long?
(a) 36 seconds
(b) 30 seconds
(c) 24 seconds
(d) 18 seconds
Train travels 150 + 500 meter in 30 second
Speed of train = 650/30
= 65/3 m/s
Now, time take to cross a platform 370 metre long
=(150+370)/(65/3)
=(520×3)/65
= 24 sec.

Q3. A passenger standing on a railway platform observes that a train going in one direction takes 4 seconds to pass him. Another train of same length going in opposite direction takes 5 seconds to pass him. The time taken (in seconds) by the two train to cross each other will be:
(a) 35
(b) 36.5
(c) 40/9
(d) None of these
Let the length of each train be x metre and the speeds of the trains are S1 and S2 respectively.
S1=x/4, S2=x/5
Now, Required time = 2x/(x/4  + x/5)
[∴ Trains are moving opposite] = 40/9 seconds

Q4. A passenger sitting in a train of length l m, which is running with speed of 60 km/h passing through tow bridges, notices that he crosses the first bridge and the second bridge in time intervals which are in the ratio of 7 : 4 respectively. If the length of first bridge is 280 m, then the length of second bridge is:
(a) 490 m
(b) 220 m
(c) 160 m
(d) Can’t be determined
Passenger sitting in a train pass through two bridges then the train will travel the only length of the bridge.
So, ratio of length of bridge = ratio of time to pass the bridge. (Distance α time)
= 7: 4
So, length of second train = (280 × 4)/7
= 160 metre.

Q5. Two guns are fired from the same place at an interval of 6 minutes. A person approaching the place observes that 5 minutes 52 seconds have elapsed between the hearing of the sound of the two guns. If the velocity of the sound is 330 m/sec, the man was approaching that place at what speed (in km/hr)?
(a) 24
(b) 27
(c) 30
(d) 36
Difference of time = 8 second
So, distance covered by 352 s (5 × 60 + 52) second by man
= distance covered by sound in 8 second
S × 352 = 330 × 8
Here S is the speed of man in m/s
S = 15/2 m/s
So, speed in km/hr
S = 15/2×18/5=27 km/hr

Q6. If the arithmetic mean of 3a and 4b is greater than 50, and a is twice of b, then the smallest possible integer value of a is
(a) 18
(b) 19
(c) 20
(d) 21
According to the question,
(3a+4b)/2 > 50
3a + 4b > 100
3a + 2a > 100 (given that a = 2b)
5a > 100
a > 20
Hence, smallest possible integer value of a = 21

Q7. A profit of 12% is made mobile phone is sold at Rs. P and there is 4% loss when the phone is sold at Rs. Q. Then Q : P is
(a) 4 : 5
(b) 3 : 1
(c) 1 : 1
(d) 6 : 7
Let the cost of mobile phone = 100
So, P = 112 Rs.
Q = 96 Rs.
Required ratio Q : P = 96 : 112 = 6 : 7

Q8. From 1980-1990, the population of a country was increased by 20%.
From 1990-2000, the populations of the country was increased by 20%.
From 2000-2010, the populations of the country was increased by 20%.
Then the overall increased population (in percentage) of the country from 1980-2010 was
(a) 60%
(b) 62.8%
(c) 72.2%
(d) 72.8%
Let the population of the country in the year 1980 = P
The overall increase in population of a country from 1980 to 2000 is = (P × 1.2 × 1.2 × 1.2 – P)/P
=(1.728P-P)/P
% increase in population = .728 ×100
= 72.8%

Q9. If the ratio of cost price to selling price is 10 : 11, then the rate of percent of profit is
(a) 0.1%
(b) 1%
(c) 1.1%
(d) 10%
Let the cost prices = 10 Rs.
Selling price will be = 11 Rs.
Profit % = (S.P – C.P)/(C.P)
=(11-10)/10=10%

Q10. A farmer travelled a distance of 61 km in 9 hours. He travelled party on foot at the rate 5km/hour and party on bicycle at the rate 9 km/hour. The distance travelled on foot is
(a) 20 km
(b) 15 km
(c) 16 km
(d) 17 km
Let distance travelled on foot = x km
According to the question,
x/4+  (61-x)/9=9
x/4-x/9+61/9=9
5x/36=9-61/9
x = 16
The distance, travelled on foot = 16 km.