Arithmetic

Time, Speed & Distance

Medium

In a flight of 1400 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 450 km/h and the time of flight increased by 60 minutes. The speed of the aircraft due to bad weather is what percent (rounded off to 2 decimal places) of the original speed of the aircraft?

57.14%

43.33%

52.28%

60.67%

✅ Correct Option: 1

Let the original speed be $x$ km/h

Reduced speed = $(x - 450)$ km/h

Distance = $1400$ km

Time increase = $60$ minutes = $1$ hour

Using Time = Distance ÷ Speed:

Original time = $\dfrac{1400}{x}$ hours

New time = $\dfrac{1400}{x-450}$ hours

Since new time is 1 hour more than original time:

$\dfrac{1400}{x-450} - \dfrac{1400}{x} = 1$

Multiplying by $x(x-450)$ :

$1400x - 1400(x-450) = x(x-450)$

$1400x - 1400x + 630000 = x^2 - 450x$

$630000 = x^2 - 450x$

$x^2 - 450x - 630000 = 0$

Using quadratic formula:

$x = \dfrac{450 \pm \sqrt{450^2 + 4 \times 630000}}{2}$

$x = \dfrac{450 \pm \sqrt{202500 + 2520000}}{2}$

$x = \dfrac{450 \pm \sqrt{2722500}}{2}$

$x = \dfrac{450 \pm 1650}{2}$

Taking positive value: $x = \dfrac{450 + 1650}{2} = 1050$ km/h

Reduced speed = $1050 - 450 = 600$ km/h

Percentage = $\dfrac{600}{1050} \times 100 = 57.14\%$

2024: Slot 1

A train running between two towns arrives at its destination 10 minutes late when it goes at 60 km per hour and 16 minutes late when it goes at 40 km per hour. Determine the speed at which the train reaches on time.

2024: Slot 2

Nidhi reached her institute in 3 hours while travelling by bus with a wheel radius of 70 cm and making 250 revolutions in one minute. One day, she left for the institute one hour later than usual time. Then to reach her institute on time, she should increase her speed by ____. [Use $\pi = \frac{22}{7}$ ]

BBA-DBE Bangalore 2025

The time taken by a boat to cover a certain distance in still water is 20% less than the time it takes to cover the same distance upstream. The speed of the stream is 4.5 km/h. How much total time (in hours) will the boat take to cover 60 km downstream and 30 km upstream?

BBA-DBE Bangalore 2026

The time taken by a boat to travel a certain distance upstream is equal to the time taken by it to travel 2.5 times the same distance downstream. The speed of the boat in still water is 7 km/h. How much time (in hours) will the boat take to travel 20 km upstream and 36 km downstream?

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