CDS MATHEMETICS QUIZ

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Question 1:

At its usual speed, a train of length $L$ metre crosses a platform $300 \mathrm{~m}$ long in $25 \mathrm{sec}$. At $50 \%$ of its usual speed, the train crosses a vertical pole in $20 \mathrm{sec}$. What is the value of $\mathrm{L}$ ?

Question 2:

A train can travel $50 \%$ faster than a car. Both start from point A at the same time and reach point B $75 \mathrm{kms}$ away from $\mathrm{A}$ at the same time. On the way, however, the train lost about $12.5$ minutes while stopping at the stations. The speed of the car is:

Question 3:

Distance between two places Delhi & Agra is $425 \mathrm{~km}$. Two persons Deepu and Sukhi start their journey from Delhi at the same time. Speed of Deepu is $55 \mathrm{~km} / \mathrm{hr}$ less than speed of Sukhi. When Sukhi reaches at Agra, he returns immediately and meet to Deepu at Mathura on the way. If distance between Agra and Mathura is $125 \mathrm{~km}$. Find the speed of Deepu?

Question 4:

The distance between two places $\mathrm{A}$ and $\mathrm{B}$ is $1090 \mathrm{~km}$. A train starts from $\mathrm{A}$ at $50 \mathrm{kmph}$ at 6 am and another train starts from B at 80 $\mathrm{kmph}$ at 7 am towards each other. At what time will they meet?

Question 5:

Two trains Vivek express and Vande Bharat start simultaneously in the opposite direction from two points Lucknow and Delhi respectively and meet at Etah after  $\mathrm{T}$ minutes and arrive at their destinations in 3 hour 45 minutes and 5 hours 24 minutes respectively. After their meeting each other Find out the value of  $\mathrm{T}$.

Question 6:

A man starts from his house and travelling at $30 \mathrm{~km} / \mathrm{h}$, he reaches his office late by 10 minutes, and travelling at $24 \mathrm{~km} / \mathrm{h}$, he reaches his office late by 18 minutes. So what is the right time (in minutes) to reach at office:

Question 7:

If varun goes to his school at the speed of 30 $\mathrm{km} / \mathrm{h}$. He reaches 1 hour early and if he travels at the speed of $25 \mathrm{~km} / \mathrm{h}$ he reaches 30 minutes early. Find out his actual speed at which he reaches school on time.

Question 8:

40 litres of petrol is required to travel 800 $\mathrm{km}$ using a $800 \mathrm{cc}$ engine car. If the volume of petrol required to cover a distance varies directly as the capacity of the engine of car, then how many litres of petrol is required to travel $1000 \mathrm{kms}$ using $1200 \mathrm{cc}$ engine car.

Question 9:

A bike travels $\frac{1}{3}$ of the distance on a straight road with a speed of $10 \mathrm{~km} / \mathrm{h}$, the next $\frac{1}{3}$ with a speed of $20 \mathrm{~km} / \mathrm{h}$ and the last $\frac{1}{3}$ with a speed of $60 \mathrm{~km} / \mathrm{h}$. What is the average speed of the bike for the whole journey?

Question 10:

Duranto Express and Vande Bharat start moving towards each other from places Delhi and Agra respectively, at the same time on the same day. After meeting on the way, Duranto Express and Vande Bharat take 7 hours 21 minutes and 10 hours 25 minutes, respectively to reach Agra to Delhi. Find out after how much time they will meet each other.