**UGC NET Mathematical Aptitude Paper-1 | Fraction | Time & Distance**

**Mathematical aptitude:- ** Testing your ability to use numbers and calculations to answer mathematical issues is known as mathematical aptitude.

Fraction :- A fraction represents a part of a total. The Latin word “fractio” which meaning “to break” is the source of the English term “fraction.” A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

For example, 5/7, 9/8, 2/5, 3/2.

1. In a class of 48 students, 1/4th of them watch cartoons. How many students do not watch cartoons ?

A. total student is 48 and 1/4th of them watch cartoons ,

so total number of student Watch cartoon is 48*1/4 = 12

so students do not watch cartoons is 48 -12 = 36

Either

48*(1-1/4)

48* 3/4 = 36

2. In a office of 75 employees, 2/3rd of them eat veg. How many employees eat non-veg ?

A. total student is 75 , 2/3rd of them eat veg.

so out of total employees 2/3rd of them eat veg 75*2/3 = 50

so employees do not eat veg is 75 -50 = 25

Either

75*(1-2/3)

75* 1/3 = 25

** Important Fraction Question for ugc net preparation and Put the answer on comment.**

1 In a office of 1500 employees, 3/5th of them playing hockey. 1/5th of them playing football and rest is playing Ludo ,How many employees is playing Ludo ?

2 In a class of 1000 students, 1/4th of them watch cartoons, 1/4th of them watch movie, 2/4th of them watch web series How many students do not watch cartoons ?

3 In a class of 1000 students, 1/4th of them watch cartoons, 1/4th of them watch movie, 2/4th of them watch web series How many students watch cartoons ?

**Speed, ****Time & Distance :-**

Speed = Distance/ Time

Time = Distance/Speed

Distance = (Speed x Time)

km/hr to m/sec conversion : x km/hr = x X 5/18 m/sec .

m/sec to km/hr conversion : x m/sec = x X 18/5 km/hr

Suppose a woman covers a certain distance at x km/hr and an equal distance at y km/hr.

Then, the average speed during the whole journey is 2xy/x + y km/hr.

Question for Example :-

1. A bus crosses a 500 m long street in 10 minutes. Find out the speed in km per hour ?

solution :-

Total distance = 500 m , total time 10 min

first we have need to convert in same unit of both distance ,and time

so Total distance = 500 m , and convert time 10 min in sec

so we will multiply 10 min * 60 = 600 sec

Speed = Distance/ Time

Speed = 500 m / 600 sec

Speed = 0.833 m/sec

now need to convert Speed = 0.833 m/sec into km/hr

m/sec to km/hr conversion : x m/sec = x X 18/5 km/hr

0.833 m/sec into km/hr = 0.833 *18/5 km/hr

his speed in km per hour = 3 km/ hr

2. A train covers a certain distance at a speed of 240 km/hr in 5 hours. To complete the same distance in 2 hours, Find out the speed

solution :-

Total distance covered by train is = (Speed x Time)

Total distance covered by train is = 240 km/hr * 5 hr

Total distance covered by train is = 1200 km

now same distance need to cover in 2 hr. so speed would be 1200 km / hr divided by 2

so speed would be 600 km / hr.

3. If a caw walks at 14 km/hr instead of 10 km/hr. he would have walked 20 km more. Find out the Distance

solution :-

difference of speed is 14 km/hr – 10 km/hr = 4 km/hr

Extra distance = 20 km

so , Time = Distance/Speed

Time = 20 km / 4 km /hr.

Time = 5 hr.

actual distance travelled = (Speed x Time)

actual distance travelled = 10 km/hr * 5 hr.

actual distance travelled = 50 km

**Important Time & Distance Question for ugc net preparation and Put the answer on comment.**

1. Saurabh complete a journey in 10 hours. He travels 50% of the journey at the rate of 10 km/hr. and rest journey at the rate of 15 km/hr. Find the total journey in km.

2. The ratio between the speeds of two trains is 3 : 5. If the second train runs 500 km in 5 hours, then what is the speed of the first train.

3. A cow on tour travels first 320 km at 32 km/hr. and the next 320 km at 40 km/hr. what is the average speed of the tour.

4. In covering a distance of 30 km, Saurabh takes 2 hours more than Sonu. If Saurabh doubles his speed, then he would take 1 hour less than Sonu. Saurabh’s speed is

5. Saurabh is travelling on his cycle and has calculated to reach point A at 3 P.M. if he travels at 15 km/ph, he will reach there at 12 noon if he travels at 20 km/ph. what speed he has required to travel to reach A at 1 P.M

6. It takes eight hours for a 500 km journey, if 120 km is done by car and the rest by motor cycle . It takes 20 minutes more, if 150 km is done by car and the rest by motor cycle . The ratio of the speed of the car to that of the motor cycle is

7. A woman travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr. and partly on motor cycle @ 9 km/hr. The distance travelled on foot is