**Mathematics Quiz for Juniors**

*1 – A man moves upstream in 6 hours in a boat at a speed of 20km/h. Then he rows down in 3 hours. What is the rate of flow of the stream?*

*20 km/h**12 km/h**15 km/h**8 km/h**10km/h*

*2 – **300 apples are equally distributed amongst a certain number of students. If there were 10 students more each will get alone one apple less. Find total number of students.*

*60**50**70**100**None of these*

*3 – If a number multiplied by 25% of itself gives a number which is 200% more than the number, then the number is*

*12**16**20**24*

*4 – **A bus can go from A to B via two routes 1 and 2 with speed kept the same. It takes 40 % more time in route 1 than in route 2. If distance of route 2 is 150 km and total fuel used in both the routes is 84 litres. Then find the difference of oil consumed in both the routes.*

*12.5 litre**13 litre**14 litre**11.5 litre**14.5 litre*

*5 – **Chords AB and CD of a circle intersect externally at P. If AB = 6 cm, CD = 3 cm and PD = 5 cm, then the length of PB is*

* *

*5 cm**7.35 cm**6 cm**4 cm*

*6 – A pipe can filled a tank in 6 hrs. After half tank is filled 3 more similar pipes are opened. What is total time taken to be filled.*

*3 hour 48 minutes**3 hour 48 minutes**3 hour 30 minutes**4 hour 40 minutes*

*7 – A shopkeeper is selling sugar at 15% profit but with 25% false weight. Find the total profit percentage.*

*33.33**53.33**45.75**60.25*

*8 – What is the ratio of distance travelled by a car going at 50kmph for 8 hours to a bike going at 37.5kmph for 4 hours to a scooter going at 22.5kmph for 6 hours?*

*80:30:25**80:31:27**80:31:29**80:30:27*

*9 – If x : y be the ratio of two whole numbers and z be their HCF, then the LCM of those two numbers is*

*xy**(xz/y)**(xy/z)**xyz*

*10) – If 7A = 5B = 2C; ﬁnd A : B : C.*

*35:14:10**14:10:35**2:5:7**10:14:35*

*1 – Solution : – e *

*As the man moves upstream in 6 hours at a speed of 20km/h, the length of the stream = Speed × Time = 20 × 6 = 120 km
So, speed of the boat downstream = Distance/Time = 120/3 = 40km/h
So, let the speed of the boat in still water be x km/h and the rate of flow of the stream be y km/h.
For upstream, x – y = 20
For, downstream, x + y = 40
On solving the above two equations, we get y = 10km/h.
So, rate of flow of the stream is 10km/h.*

*2 – Solution : – b*

*Let total number of student = x
According to question.
From option x = 50 satisfy the given equation.*

*3 – Solution : a*

*Let the number be x. Remember the given number is 200% more than the original so, new number will be 300% of the original one.
*

*4 – **Solution : c*

*As the speed of the bus is same so distance of route 1 = 40 % more than route 2.
Distance of route 1=1.4*150=210 km
As the fuels used in routes is directly proportional to the distance travel in the routes.
The ratio of fuel used in different routes= ratio of the difference of two routes.
Ratio of fuel used in different routes=210:150=7:5
Let, fuel in route 1 = 7x
Fuel in route 2 = 5x
Total fuel = 84
*

*⇒*

*12x=84*

*⇒*

*x=7*

Fuel used in route 1 = 49 litre

Fuel used in route 2 = 35 litre

Required difference = 49-35=14 litre

Fuel used in route 1 = 49 litre

Fuel used in route 2 = 35 litre

Required difference = 49-35=14 litre

*5 – b *

*6 – Solution : – b *

*A can fill it in 6 hours than we consider 6 is total work and A’s 1 hour work =1
ATQ. Half tank is filled by A
=3 hours
Remaining 3 by 4 pipes, so 3/4 more time
Total time = 3 hours + 3/4 hours
=3 hours 45 minutes*

*7 – Solution : – b *

*Let the cost price 1 kg sugar be Rs. x.
A shopkeeper is selling sugar at 15% profit but with 25% false weight.
That means, he is selling 750gm instead of 1000gm.
So, the cost price of 750gm sugar = Rs. x × (750/1000) = Rs. 3x/4
But he is taking the price of 1 kg sugar with 15% profit.
So, the selling price of 1 kg = Rs. x × (115/100) = Rs. 23x/20
Then, the profit = Rs. (23x/20) – (3x/4) = Rs. 2x/5
*

*∴*

*The profit percentage = [(2x/5)/(3x/4)] × 100 = 53.33.*

*8 – Solution : d*

*Distance travelled by the car = 50 * 8 = 400km
Distance travelled by the bike = 37.5 * 4 = 150km
Distance travelled by the scooter = 22.5 * 6 = 135km
Ratio of distance travelled = 400:150:135 = 80:30:27*

*9 –** Solution : d*

*First no. x Second no. = L.C.M. x H.C.F.
So, L.C.M. = zxy*

*10 – **Solution : – d *

*Given: 7A = 5B = 2C. Therefore,
A/B = 5/7 and B/C = 2/5
Hence A/B = 10/14 and B/C = 14/35
Therefore,
A : B : C = 10 : 14 : 35*