Time, Speed, Distance and Work Solved Problems  
I have been suffering from the writer's block lately
and therefore I decided to do what I like to do the most solving problems. To
help all the CAT 2010 aspirants on Total Gadha, I decided to hunt TG quant forum
for the time, speed and distance problems and solve them. What a treasure I
discovered! Some of these problems will baffle brains of even some of the most
experienced instructors. I am posting all the problems I solved along with
their solutions. All of you please first try to solve the problems on your own
and then see the solutions. This way, you would appreciate the solution to many
of these problems. Also, notice that I again used only ratios to solve these
problems. Still no equations. I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week. You might also like: Relative Speed, Clocks and Circular Motion Time, Speed and Distance 
Re: Time, Speed, Distance and Work Solved Problems  
hey sir you are genius keep continuing this.it is very useful for us. 
Re: Time, Speed, Distance and Work Solved Problems  
Hi TG, Thanks a Zillion! SP

Re: Time, Speed, Distance and Work Solved Problems  
thanks It's a great gamut of TSD .... thanks again for jiffy take care 
Re: Time, Speed, Distance and Work Solved Problems  
hey TG! shoudnt the answer in second last problem be 16? As, n(n+1)w/2=129w, for n=16, n(n+1)/2=16x17/2 =8x17 =136 >129 
Re: Time, Speed, Distance and Work Solved Problems  
hi TG, i saw it coming... the one compiled source ll definitely help a lot... thanks ll be a too common wod to say... 
Re: Time, Speed, Distance and Work Solved Problems  
Hi Purav, Corrected! Total Gadha 
Re: Time, Speed, Distance and Work Solved Problems  
Hi TG Hope u r doing gr8 as usual...nice topic... 1 doubt in 1st question is it not possible that point T is between M and S....??? 
Re: Time, Speed, Distance and Work Solved Problems  
Hi Gullz, If A is traveling for a longer time with his normal speed, he will travel a longer distance, no? Total Gadha 
Re: Time, Speed, Distance and Work Solved Problems  
In wall wala Question,what would be the mathamatical formula formed? 
Re: Time, Speed, Distance and Work Solved Problems  
So silly of me thanks Sir..... 
Re: Time, Speed, Distance and Work Solved Problems  
HI TG SIR, D ANSWER 2 D 4TH QUESTION "D DISTANCE BETWEEN MR SHARMA'S HOUSE 2 OFFICE Z INCOMPLTE.SIR PLZ REPLY IT. 
Re: Time, Speed, Distance and Work Solved Problems  
Hi Ankit, Both points taken. Total Gadha 
Re: Time, Speed, Distance and Work Solved Problems  
There is no Timenwork question here. Sir, pls post some article on TW. 
Re: Time, Speed, Distance and Work Solved Problems  
Hi TG, can i suggest you something please add DI and DS lessons also ..as you have quants and verbal lessons Hey!, What kind of person are you? I'm surprised about  How can you manage to hit the nail on the head of the exact cause of problem? I tell you one truth, after going thru this site i felt that you have made this site only and only to help me out This is the one of the best site, I ever seen on the net. Thank You! Regards, ankita sharma

Re: Time, Speed, Distance and Work Solved Problems  
hi gmatblr, please read the solution again. in oncase distance traveled by B is 2d whereas in the second case it is 2d  d/4 Total Gadha 
Re: Time, Speed, Distance and Work Solved Problems  
tg , why have u solves the question using hpothetical assumptions [3x/2..,etc .] plz xplain. thanking u in anticipation. 
Re: Time, Speed, Distance and Work Solved Problems  
TG Sir, Thank u sooooo mch for such a wonderful article... Shiva 
Re: Time, Speed, Distance and Work Solved Problems  
these are the best questions ,, almost of the kind that we see in CAT papers. thanks a lot man.. )) this site has made my office hours BLISS :P 
Re: Time, Speed, Distance and Work Solved Problems  
it doesnot have to meet at the point s.b wil still cover the same distance 2d in that time n with its normal spd wil cover d+3x/2. 
Re: Time, Speed, Distance and Work Solved Problems  
Hey Nikhil, The minute hand chases the hour hand at a speed of 11/2 degrees/min. You can find the related explanation here. At Noon both the hands are together. At One o'clock the angle diff is 30 deg. Now for a angle diff of one degree the mintue hand has to traverse either 29 or 31 degrees at a relative speed of 11/2 deg/min. The time taken would be 29*2/11 and 31*2/11 respectively. Both are nonintegers so ruled out. We now check all such cases i.e 59*2/11 and 61*2/11 for 2 o'clock, 89*2/11 and 91*2/11 for 3 o'clock and so on .. Two such cases yield integral values  121*2/11 [(30*4+1)*2/11] and 209*2/11 [(30*71)*2/11]. Hence answer is 2. 
Re: Time, Speed, Distance and Work Solved Problems  
Dear TG Sir, I recently came to know about your site. I am really thankfull to you for posting a wide range of topics. Regards, 
Re: Time, Speed, Distance and Work Solve this Simple Problem ?????????  
Hi Pallavi

Re: Time, Speed, Distance and Work Solved Problems  
Hi Kanika, answer is 1 km/hr. solution: let u and v be the speed of the water and speed of the swimmer respectively.
[where, d2 distance travelled by the swimmer in half an hour.] also the time required for the cork to reach the bridge can be written as: since cork and swimmer arrive at the bridge at the same time we can equate both the equation. also d2 ( distance travelled in half an hour) can be written as : d2 = (vu) *(1/2)  (2) replacing d2 in equation 1, we get (1/2) + ((vu)/2(u+v)) + (1/(u+V)) = (1/U) solving the equation we get u=1 cheers and beers .. 
Re: Time, Speed, Distance and Work Solved Problems  
hey thanx pravin but i cudnt get this step.... (1/2) + (d2/(u+v)) + (1/(u+V)) why you have added 1/2 : what is this 1/2 kanika 
Re: Time, Speed, Distance and Work Solved Problems  
1/2 is the half hour which the swimmer swam after crossing the cork and reached the point from whr he traveled back 
Re: Time, Speed, Distance and Work Solved Problems  
Hi TG, In the first question, i am unable to figure out ur calculating for the first case where distance travelled by A is d+3x/2 and by B is 2d. If A travels more than the distance x, then the distance travelled by B should be 2d(x/2). Similarly for the second case: distance travelled by A should be (11d + 10x)/8 and distance travelled by B should be (7d/4)((d+2x)/8)= (13d2x)/8. This on solving further does not yield the correct result. Please help.
Thanks!! By the way great work!! 
Re: Time, Speed, Distance and Work Solved Problems  
Any one can help me to solve this problem.....
If 20 men or 25 women or 30 boys can do a piece of work in 16 days by working 10 hours a day, then how many men with 10 women and 18 boys can do 3 ¼ times the same work in 26 days by working 8 hours daily? 
Re: Time, Speed, Distance and Work Solved Problems  
its a work problem from quantum cat by sarvesh kumar verma In a nutbolt factory 180 workers are working for 6 hrs a day. Out of 180 workers there are some men,some women and rest are boys. All the workers can produce either nut or bolt or both of them. A man can produce 60 nuts and 80 bolts in each hour and a woman can produce 30 nuts and 60 bolts per hr. A man is thrice as efficient as a boy and 3/2 times as a woman. given that all men,all women and all boys produce equal number of articles of one kind (i.e., either nut or bolt) per hour. 1. working 6 hrs a day, how many nuts they can produce with 52500 bolt in each day? a) 17500 b) 26250 c)50850 d)can't be determined 2. in how many hours can 15 men,12 women and 8 boys can produce 12000 nuts and 8200 bolts? a)3 b)5 c) 6 d) none of these 3) if 30 women and 50 boys can produce 5400 bolts in one hour then to produce equal number of nuts in one hour how many men are required? a)30 b)40 c)50 d) none of these 4) if the manager of the factory wanted equal number of men, women and boys in his factory but the efficiency of a man,woman and a boy remains constant, then the change in production is a)increased by 10% b)decreased by 10% c) increased by 8.33% d)none of these 
Re: Time, Speed, Distance and Work Solved Problems  
HI TG, I need your guidance regarding my situation.. I read somewhere on net that IIMA gives a lot of consideration to 10th & 12th marks... is it true?? I got 80% in 10th, but 60% in 12th. Ive done B.Tech in computer science with distinction (73%).. If I crack CAT with a very high percentile (say 99.8) and clear all sectional cutoffs with a year's work ex, then do i have a chance to recieve a call from IIMA??? Also I am dead serious about CAT 2010.. Im working as a software developer and reach home 10 at night and leave at 7 (due to my long travel time).. How do i utilize the limited time ive got in most appropriate way??? Also I drive for around 2 and half hours (up & down included), how can I utilise this time? I mean do u have any audio files which can be useful??? Please reply back, it would be reallyyyyyyyy appreciated.. Thanks & Regards, Amar 
Re: Time, Speed, Distance and Work Solved Problems  
answer to the question MR.SHARMA is 15 k.m. After estimating that mr.sharma will take 75 min. to reach his office at his normal speed , lets assume his normal speed is x kmph , we know 75 min. = 60 min. + 15 min. = 1 hour + 1/4 hour = 5/4 hours , now his speed after 50% increament would be x + x/2 = 3x/2 kmph, now Speed * Time = Distance , 3x/2* 5/4 = distance ,i.e. 15x/8 = distance , going by the options ,which are 10, 15 , 5 , 20 and 25 only 15 is possible since any other options are not multiple of 15. only 15 is possible when x = 8 . 
Time, Speed, Distance and Work Solved Problems  
TG Sir, Can u please explain the relation u established between d and x in the first question more clearly Regards, Jyothsna 
Re: Time, Speed, Distance and Work Solved Problems  
Please help me with this problem: In a kilometer race, Ram beats Shyam by one minute and Shyam beats Tarun by 30 seconds. If Ram beats Tarun by 250m in the same race. Find the time taken by Ram to run the race (in seconds). ans; 270 
Re: Time, Speed, Distance and Work Solved Problems  
Please tell me where i am wrong in the below solution:? Also, the common question: a car had to travel a total distance of 600 km. after travelling a part of the distance, it developed an engine problem. It travelled the remaining distance at 4\5 of the speed.It arrived an hour late.Had the engine problem occurred after it had travelled 150 more km then it reached half an hour earlier.Find the distance it travelled without any problem. Let it travel at S speed and the distance be D from where it broke down. so s/(4/5s)=t+1\t =>t=4 hrs so now D150\D=(t+1\2)\t+1 
Re: Time, Speed, Distance and Work Solved Problems  
Hi Neha
That's a very easy question. Just see that if Ram takes 't' minutes to finish 1km (1000 m), then Shyam takes 't+1' and Tarun takes 't+1.5' minutes respectively. Also it is given that Ram beats Tarun by 250 m i.e. Tarun can travel the remaining 250 m in 1.5 m i.e. 90 seconds. So Tarun must have taken 3*90 = 270 seconds to travel 3*250m = 750m distance in the same time in which Ram has travelled the complete distance of 1km = 1000m. So answer is 270 seconds. Kamal Lohia 
Re: Time, Speed, Distance and Work Solved Problems  
HI sagar, Ans=30 since men required: total work= 20X16X10 MDH New total work= (13/4)X20X16X10= 13X50X16 since wd by 20 men or 25 women or 30 boys is same m:w:b = 4:5:6 Therefore, 10 women = 8 men & 18 boys= 12 men, so 20 men are there (20+ExtraMen) X 26days X 8hrs = 13 X 50 X 16 mendayhrs ExtraMen=30

Re: Time, Speed, Distance and Work Solved Problems  
Thank TG, For such a useful article.But i think,In the 7th question, 2nd method of solution, the value of v should be 60. so that when we multiply v and t then answer will be 300. U r Genius.... 
Re: Time, Speed, Distance and Work Solved Problems  
Hi TG, 'Dog for a Walk' Problem can be easily solved using options..similar technique which you used in one of the articles 'Shortcut for quants'. For the First meeting point the ratios of thier speeds will be equal to ratios of their distances covered. If V be the speed of Dog then 4/v = d1/(625+625d1)>1 where d1 is the distance travelled by the man till the first meeting point. Now lets check the options of the second question  for distance covered by dog to be 1000  d1 has to be 250. substituting in 1 we get 4/v = 250/1000 v = 16 which is among the options in the first question. Similarly we can see that none of the other options satisfy. Btw why TG.com is so descolated? Guys Lets activate Faiyaz 
Re: Time, Speed, Distance and Work Solved Problems  
can anyone please explain me the wall problem here in the article.. 
Re: Time, Speed, Distance and Work Solved Problems  
Hi Kirti, Concept is simple. the wall will grow only when Added lengh is more than that of falling. lets take the wall Length to be 8m. Then 1/8 length = 1 m is build every day and 20% of the length build till that day is demolished. So when the length of the wall reaches 5m, at the end of the day the wall demolised will be 20% of 5m = 1m which is the length build on that day. so new wall length will be 4m. now whenever 1m is added 1m is demolished. hence the wall remains at 4m. i hope its clear
Faiyaz 
Re: Time, Speed, Distance and Work Solved Problems  
I have a query Raj and Neetu leaves form college together to their home.Raj travles on Cycle and Neetu walks on foot with different speeds.Raj travels towards their home and return back to neetu. After third round they walks 27m together with same speed. If speed of Neetu is 4km/h duirng her walk and The distance between their house and college Gate is 125 then Find Speed of Raj. 
Re: Time, Speed, Distance and Work Solved Problems  
Vaibhav, The question is not clear. How come they are 'walking together' in the third round? Isn't Raj traveling on bicycle? And what does 'third round' mean? 
Re: Time, Speed, Distance and Work Solved Problems  
I have a doubt in 1st question,as explained if A travels d+3x/2 and B travels 2d,that means distance between A and B is d+3x/2+2d i.e 3d+3x/2 whereas it actually is 3d+x..Can anyone please explain thi to me :O 
Re: Time, Speed, Distance and Work Solved Problems  
plz provide the solution for this question 
Re: Time, Speed, Distance and Work Solved Problems  
let asssume the distance between college & home is = d when they meet first time let the distance from home to neetu is= x then distance covered by raj=(d+x) distance covered by neetu= (dx) if their speed is v1 & v2 respectably then v1/v2=k=(d+x)/ (dx) or, x=d(k1)/(k+1) for third round it will be {d(k1)/(k+1)}^3 = 27=3^3 or k=4 therefore speed of raj is=4*4= 16 km/hr 
Re: Time, Speed, Distance and Work Solved Problems  
need help understanding this question pls respond: A starts at a point P, on a circular track of length 10 km, at 6 am and runs at a speed 3u km/hr in the clockwise direction. B starts running at a speed of 2u km/hr from Q, the point diametrically opposite to P at 6:05 am, in the opposite direction. If u is less than 30, at how many distinct points do A and B meet on the track? a)3 b)5 c)6 d)cannot be determined 
Re: Time, Speed, Distance and Work Solved Problems  
Answer for the 4th question is 25kmph let usual speed= 100 kmph and time = t and distance = 100*t km ...(1) In frst condition new speed s1=125kmph new time t1= t(usual time)+15/60 and distance = 125*(t+15/60) km ...(2) And in second cndtn new speed s2= 375/2kmph new time t2= t5/60 and distance = (375/2)*(t5/60) km ...(3) frmeq (2) & (3) t = 1/4 hour then frm eq(1) distance = 100*1/4 = 25 kmph 
Re: Time, Speed, Distance and Work Solved Problems  
Can anyone help me with this Question?? Arun took part in a triathlon, an athletic event. he had to swim, run and bicycle to 10km , 24km and 30km respectively and return the same way. Arun's average speed for the triathelon is 4 Km/h. he took a total of 4 min for swimming and 20 min for bicycling in the triathelon. His speed of running is : a) 5km/min b) 6km/min c) 7.5km/min d) 8/3 km/min P.S.  I guess, this is a wrong Question. 