Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

A cyclist, after riding a certain distance, stopped for half an hour to repair his bicycle, after which he completes the whole journey of 30 km at half speed in 5 hours. if the breakdown had occured 10 km farther off, he would have down the whole journey in 4 hours. find where the break down occured and his original speed.
 
Asked by maragadhasudha | 11 Aug, 2015, 07:25: PM
answered-by-expert Expert Answer
The two cases are shown in the figure above.
In the first case, the breakdown occurs at point B, where the cyclist stops for half an hour. 
Let the distance travelled before breakdown be X(AB) as shown in the figure. Then, the remaining distance BD=30-X.
Speed from A to B is 2V and speed from B to C is V.
In the second case, the breakdown occurs at point C which is 10 km farther off from point B as shown in the figure.  
Speed from A to C is 2V and speed from C to D is V.
As we can notice, in both cases, the only difference is the speed with which the cyclist goes from B to C. 
In the first case the speed from B to C is V and in the second case the speed from B to C is 2V. 
From A to B and from C to D , the speeds remain the same in both cases. 
Hence, the difference in time of travel in both cases is due to the difference in speed from B to C only. 
From B to C , the speed becomes twice from case 1 to case 2 with distance remaining the same. Hence, time will be halfed. 
If 't' is the time taken to go from B to C in case 1, then the time taken to go from B to C in 2nd case will be t/2.
Hence, the difference in time of travel from B to C is t - t/2 = t/2. 
This has to be the difference in time for the whole journey as well because the speed remains the same for remaining parts.
Hence, t/2 = 5-4 = 1 hr. 
t= 2 hours......(1)
Hence, in the first case the cyclist travels from B to C in 2 hours. 
Distance from B to C is 10 km. Hence, speed from B to C in 1st case = 10 / 2 = 5 kmh.
Hence, in the first case speed from B to D is 5 kmh.
Speed from A to B is twice of that. Hence, speed from A to B is 10 kmh.
Now, the time taken for repair of cycle is half an hour. 
Hence, the actual time of travel is 5 - 0.5 = 4.5 hour. 
T subscript A D end subscript equals T subscript A B end subscript plus T subscript B D end subscript rightwards double arrow 4.5 equals X over 10 plus fraction numerator 30 minus X over denominator 5 end fraction rightwards double arrow 45 equals X plus 60 minus 2 X rightwards double arrow X equals 15 space k m H e n c e comma space t h e space b r e a k d o w n space o c c u r e d space a t space a space d i s tan c e space o f space 15 space k m space f r o m space t h e space s t a r t space o f space j o u r n e y space a n d space t h e space o r i g i n a l space s p e e d space i s space 10 space k m h.
Answered by satyajit samal | 12 Aug, 2015, 10:22: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
Present age of 'A' is 4 years less than that of 'B'. Age of 'C', 4 years hence from now will be 60% more than the age of 'B', 4 years ago from now. Find the present average age of 'A' and 'B' together if the sum of present age of 'A' and 'C' is 48 years.
Asked by jhajuhi19 | 01 Feb, 2024, 08:43: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Data given below is related to daily routine [study time (in hours), entertainment time (in hours) and rest time (in hours)] of three students A, B and C.    Daily routine (24 hours) = Study time + Entertainment time + Rest time   A's study time is 1 hour less than B's study time and A's rest time is 7 hours more than his entertainment time. Ratio of A's entertainment time to B's entertainment time is 1: 2. Average of study time of A, B and C is 6 hours. Average of rest time of A and B is 9 hours. Ratio of C's entertainment time to his rest time is 4: 3.   If B's study and entertainment time is m% more than C's study and entertainment time together, then find that B's study and entertainment time together is what percent more than A's study and entertainment time together?
question image
Asked by jhajuhi19 | 31 Jan, 2024, 11:21: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
the numerator of fractions is 4 less than the denominator. if the numerator is decreased by 2 and the denominator is increased by 1 , then the denominator is 8 times the numerator. find the fraction.
Asked by am.mansi628 | 29 Nov, 2023, 05:38: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
solve this
question image
Asked by simmysingh1aug | 21 Sep, 2023, 01:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
M alone a work comppet in 50 days the same work N complet in 100 days then they both are complet 25 days then what percent work the total work will be completed
question image
Asked by bhaveskumar9938 | 08 Jul, 2023, 05:40: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
maths
question image
Asked by krishpatel20108 | 01 Jan, 2023, 07:56: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
worksheet 1 question 1
question image
Asked by bhawnabansal47809 | 01 Jun, 2022, 07:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
exceeds it's bredth by 3m
Asked by preetijain4723 | 27 Apr, 2022, 09:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
pls solve this math doubt
question image
Asked by dhruvdilipschool | 07 Mar, 2022, 11:37: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
A and B together can do a piece of work in n days while B alone can finish in it m days.work done by A in 1 days is   
Asked by Senorita | 30 Dec, 2021, 11:23: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×