Latest TCS Aptitude Question SOLUTION: A and B run a 1000 m race. if A gives B a start of 50 m, A wins by 14 sec. If B gives A start of 22 sec B wins By 20 m. Find time taken by A to complete the race.

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A and B run a 1000 m race. if A gives B a start of 50 m, A wins by 14 sec. If B gives A start of 22 sec B wins By 20 m. Find time taken by A to complete the race.

Asked In TCS (11 years ago)

Solved Pritesh Saurav Read Solution (8)

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Read Solution (8) :

Pritesh Saurav  (11 years ago)

case 1: A (dist)= 1000;
A (time)= t1;
B (distance) = 950;
B(time) = t1+14
and
case 2:
A(dist)= 980;
A(time)= t2;
B(dist)=1000;
B(time)= t2+22;
then,
speed of A= 1000/t1=980/t2
= t2= 980*t1/1000 -----(1)
and
speed of B= 950/(t1+14)=1000/(t2+22) ------(2)
put eq (1) in eq (2)
we get t1=100sec

Is this solution Helpfull? Yes (27) | No (8)  

Pratyusha Bhadra  (11 years ago)

@pritesh according to the question B gives A a start of 22sec.so dont u thnk that in case 2 velocity of B shld be 1000/(t2-22)?plz let me knw if i am wrng...

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swati  (11 years ago)

Let speed of A and B be a and b m/sec.
Time taken to cover 1000m by A = 1000/a
Time taken to cover 950m by B = 950/b
Now 950/b - 1000/a = 14 - Eqn 1

Also 980/a + 22 = 1000/b,
1000/b - 980/a = 22 - Eqn 2

Let 1/a = x and 1/b=y,
950y - 1000x = 14 and
1000y - 980x = 22

Solving, x=1/10 and a = 1/x =10m/s
Time taken by A to run 1km = 1000/10 = 100 seconds.

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Pritesh Saurav  (11 years ago)

distance time
case 1: A - 1000 t1
B - 950 t1+14
case 2: A - 980 t2
B - 1000 t2+22
now,
speed of A= 1000/t1=980/t2
= t2= 980*t1/1000 -----(1)
and
speed of B= 950/(t1+14)=1000/(t2+22) ------(2)
put eq (1) in eq (2)
we get t1=100sec

Is this solution Helpfull? Yes (5) | No   

Guru Pranav  (11 years ago)

100 Sec.

Is this solution Helpfull? Yes (3) | No (3)  

rohit  (11 years ago)

Let speed of a and b are A and B resp..
case 1
time taken by a=1000/A SEC.
time taken by b=(1000/A)+14(In 950mt.)
distance equation for b
[(1000/A)+14]*B+50=1000
so, b=950/[(1000/A)+14]......(1)
case 2
time taken by a=22+980/A
distance equation for b
[22+980/A]*B=1000
[22+980/A]*{950/[(1000/A)+14]}=1000
[22+980/A]/[(1000/A)+14]=20/19
A=10m/s
time taken by a=1000/10=100sec.

Is this solution Helpfull? Yes (2) | No   

Swati Gokhale  (11 years ago)

Case 2 : When B = 1000 m , A = 980m and B wins by 22 sec
i.e. A takes 22 sec to complete 50 m
i.e. A completes 1 m in 22/20 = 1.1sec
thus 1000 m in 1.1 * 1000 = 100 sec

Is this solution Helpfull? Yes (2) | No (1)  

satyam shivam  (11 years ago)

a/b=1000/950-14b=980/1000-22b
after solving we get b=8.33
1000/950-14(8.33)=x/8.33
after solving,
we get
x=10
so,finally 1000/10
that is,100 is ans.

Is this solution Helpfull? Yes (2) | No   

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