Arithmetic

Time, Speed & Distance

Medium

applied

A boat takes 1 hour 30 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 km/hr, then the speed of the stream is:

2 km/hr

3 km/hr

3.5 km/hr

4 km/hr

✅ Correct Option: 1

Let the speed of the stream $= x$ km/hr

Downstream speed $= (10 + x)$ km/hr

Upstream speed $= (10 - x)$ km/hr

Time difference $= 1$ hr $30$ min $= \dfrac{3}{2}$ hours

Since Time $= \dfrac{\text{Distance}}{\text{Speed}}$ :

$\dfrac{36}{10 - x} - \dfrac{36}{10 + x} = \dfrac{3}{2}$

Taking LCM on the left side:

$\dfrac{36(10 + x) - 36(10 - x)}{(10 - x)(10 + x)} = \dfrac{3}{2}$

$\dfrac{36 \times 2x}{100 - x^2} = \dfrac{3}{2}$

$\dfrac{72x}{100 - x^2} = \dfrac{3}{2}$

$144x = 3(100 - x^2)$

$144x = 300 - 3x^2$

$3x^2 + 144x - 300 = 0$

$x^2 + 48x - 100 = 0$

$(x + 50)(x - 2) = 0$

$x = -50$ or $x = 2$

Since speed cannot be negative, $x = -50$ is rejected.

Therefore, the speed of the stream $= 2$ km/hr.

2026: 21 May Shift 2

In a 200 meter race, Taniya beats Geetansh by 40 meters or by 10 seconds. The time taken by Taniya to complete the race will be:

2026: 18 May Shift 2

Let the speed of a boat in still water be $u$ km/hr and the speed of the water current in a river be $v$ km/hr. If a man rows distance $D$ down stream and same distance upstream, then average speed of total journey is

2023: 15 June Shift 2

A motor boat covers 16 km in 2 hours downstream and 14 km in 2 hours upstream. The speed of the motor boat is :

2026: 22 May Shift 1

In a kilometer race, A beats B by 30 seconds and B beats C by 15 seconds. If A beats C by 180 m, then

Match List-I with List-II

List-I	List-II
(A) Time taken by A to run 1 km	(I) 250 seconds
(B) Time taken by B to run 1 km	(II) 45 seconds
(C) Time taken by C to run 1 km	(III) 235 seconds
(D) A beats C by	(IV) 205 seconds

Choose the correct answer from the options given below:

2025: 2 June Shift 1

In a kilometer race P runs at 10 m/sec, Q runs at 5 m/sec then which of the following statement(s) is/ are correct ?

(A) P wins the race in 100 sec

(B) Q wins the race in 100 sec

(D) Q defeats P by 500 m

Choose the correct answer from the options given below:

2026: 29 May Shift 1

The speed of a boat in still water is 12 km/hr. It takes twice as long to go upstream to a point as to return downstream to the starting point, then the speed of the stream is :

A boat takes 1 hour 30 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 km/hr, then the speed of the stream is:

Solution

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