Arithmetic

Time, Speed & Distance

Hard

A boy covers a certain distance on a toy train. If the train moved 4 kmph faster, it would take 30 minutes less. If it moved 2 kmph slower, it would have taken 20 minutes more. The distance is

40 km

50 km

60 km

80 km

✅ Correct Option: 3

Let original speed = $s$ kmph

Distance = $D$ km

Original time = $t$ hours

For original journey:

$\frac{D}{s} = t$ ...(1)

For faster speed (+4 kmph):

$\frac{D}{s+4} = t - \frac{1}{2}$ ...(2)

For slower speed (-2 kmph):

$\frac{D}{s-2} = t + \frac{1}{3}$ ...(3)

From (1): $D = st$

Substituting in (2):

$\frac{st}{s+4} = t - \frac{1}{2}$

$st = (s+4)(t - \frac{1}{2})$

$st = st + 4t - \frac{s}{2} - 2$

$\frac{s}{2} + 2 = 4t$ ...(4)

Substituting in (3):

$\frac{st}{s-2} = t + \frac{1}{3}$

$st = (s-2)(t + \frac{1}{3})$

$st = st + \frac{s}{3} - 2t - \frac{2}{3}$

$2t + \frac{2}{3} = \frac{s}{3}$ ...(5)

From (4): $s = 8t - 4$

From (5): $s = 6t + 2$

Equating:

$8t - 4 = 6t + 2$

$2t = 6$

$t = 3$

Substituting $t = 3$ in $s = 6t + 2$ :

$s = 6(3) + 2$

$s = 18 + 2$

$s = 20$ kmph

Therefore:

Distance = $st = 20 × 3 = 60$ km

JIPMAT 2024

Ram and Shyam run a race between points $A$ and $B, 5 \mathrm{~km}$ apart. Ram starts at 9 AM from A at a speed of $5 \mathrm{~km} / \mathrm{hr}$ , reaches $B$ and returns to $A$ at the same speed. Shyam starts at $9: 45 \mathrm{AM}$ from $\mathrm{A}$ at a speed of $10 \mathrm{~km} / \mathrm{hr}$ , reaches $B$ and comes back to $A$ at the same speed.

At what time do Ram and Shyam meet each other ?

JIPMAT 2024

A person travels three equal distances at a speed of 'a' $\mathrm{km} / \mathrm{hr}$ , 'b' $\mathrm{km} / \mathrm{hr}$ and ' $c$ ' $\mathrm{km} / \mathrm{hr}$ respectively. What is the average speed for the whole journey?

JIPMAT 2026

Three rings complete 60, 36 and 24 revolutions in a minute. They start from a certain point in their circumference down wards. By what time they come together again in the same position?

JIPMAT 2022

Given below are two statements based on the following:

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours.

Statement I: Speed of the boat in still water is 12 km per hour.

Statement II: Speed of the stream is 4 km per hour.

In the light of the above statements, choose the correct answer from the options given below:

JIPMAT 2024

Ram and Shyam run a race between points $A$ and $B, 5 \mathrm{~km}$ apart. Ram starts at 9 AM from $A$ at a speed of $5 \mathrm{~km} / \mathrm{hr}$ , reaches $B$ and returns to $A$ at the same speed. Shyam starts at $9: 45 \mathrm{AM}$ from $\mathrm{A}$ at a speed of $10 \mathrm{~km} / \mathrm{hr}$ , reaches $B$ and comes back to $A$ at the same speed.

At what time does Shyam overtake Ram ?

JIPMAT 2023

Aman takes half the time in rowing a certain distance downstream than upstream.
Statement (I): Ratio of the speed of the boat in still water to the speed of the water current is 2: 1.
Statement (II): If the speed of the boat in still water is 6 km per hour, then the speed of the water current is 2 km per hour.
Choose the most appropriate answer from the options given below.

A boy covers a certain distance on a toy train. If the train moved 4 kmph faster, it would take 30 minutes less. If it moved 2 kmph slower, it would have taken 20 minutes more. The distance is

Solution

Related questions:

Keyboard Shortcuts

JIPMAT Past Year Questions (Topic-Wise)