AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

An aeroplane left 30 minutes later than its scheduled time; and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/hour from its usual speed. What will be its usual speed?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

550 km/hr

650 km/hr

850 km/hr

750 km/hr

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given,
Total distance= 90 km .
Time=30 minutes less time when its speed =

250 k m / h r

more than the original speed.
Considering the speed of the aeroplane as

xkm/hr

and the distance covered= 1500 km in

t

hours.
Substituting distance=1500, speed=

x

and time=

t

in the equation

x = 1500 t

,
We know that,

30 minutes = 12 hours

Now again substituting distance=1500, speed=

x + 250

and time=

t − 12

in the equation

speed= distance time

⇒ x + 250 = 1500 t − 1 2 ⇒ x + 250 = 1500 2 t − 1 2 ⇒ x + 250 = 3000 2 t − 1

Substituting

x

1500 t

in the equation

x + 250 = 3000 2 t − 1

⇒ 1500 t + 250 = 3000 2 t − 1 ⇒ 1500 + 250 t t = 3000 2 t − 1 ⇒ 1500 + 250 t 2 t − 1 = 3000 t ⇒ 3000 t − 1500 + 500 t 2 − 250 t = 3000 t

⇒ − 1500 + 500 t 2 − 250 t = 0 ⇒ 2 t 2 − t − 6 = 0 ⇒ 2 t 2 − 4 t + 3 t − 6 = 0 ⇒ 2 t t − 2 + 3 t − 2 = 0

⇒ t − 2 2 t + 3 = 0 ⇒ (t − 2) = 0 ⇒ t = 2 ⇒ 2 t + 3 = 0 ⇒ t = − 32

Since time cannot be negative, we take the positive value of t.
Substituting t=2 in the equation

x = 1500 t

⇒ x = 15002 ⇒ x = 750 k m / h r

Thus the original speed of the aeroplane will be

750 km/hr

.
Therefore the correct option is 4.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

best study material, now at your finger tips!

live classes
progress tracking
24x7 mentored guidance
study plan analysis

download the app

An aeroplane left 30 minutes later than its scheduled time; and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/hour from its usual speed. What will be its usual speed?

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App