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Question 1 of 5
1. Question
In a race A, B and C take part. A beats B by 30 m, B beats C by 20 m and A beats C by 48 m. Which of the following is/are correct?
 The length of the race is 300 m.
 The speeds of A, B and C are in the ratio 50:45:42.
Select the correct answer using codes given below.
Correct
Ans: C
 Let the length of race be x m
Then, distance covered by A = xm.
Distance covered by B when A reaches the destination =x30
Distance covered by C when A reaches the destination = x48
and distance covered by C when B reaches the destination =x20
(x30)/x =(x48)/x20) ⇒ x^{2} 50x+600=x^{2}48x
∴x = 300m
 The speeds of A,B and C are in the ratio
300: 270:252= 50: 45: 42
Incorrect
Ans: C
 Let the length of race be x m
Then, distance covered by A = xm.
Distance covered by B when A reaches the destination =x30
Distance covered by C when A reaches the destination = x48
and distance covered by C when B reaches the destination =x20
(x30)/x =(x48)/x20) ⇒ x^{2} 50x+600=x^{2}48x
∴x = 300m
 The speeds of A,B and C are in the ratio
300: 270:252= 50: 45: 42

Question 2 of 5
2. Question
A motor boat, whose speed is 15km/h in still water goes 30 km downstream and comes back in a total of 4 h and 30 min. The speed of the stream is
Correct
Ans: b
Let speed of stream be x km/h.
Speed of boat in downstream= (x + 15) km/h
Speed of boat in upstream= (15x) km/h
Total time taken= 4h 30 min
∴ 30/(x+15)+[30/(15x)]=4(1/2)
30(15x+15+x)/(15^{2}x^{2}) = 9/2
30(30)/225x^{2} =9/2
200 = 225 – x^{2}
X^{2} = 25
X=5km/h
Hence, speed of stream= 5 km/h
Incorrect
Ans: b
Let speed of stream be x km/h.
Speed of boat in downstream= (x + 15) km/h
Speed of boat in upstream= (15x) km/h
Total time taken= 4h 30 min
∴ 30/(x+15)+[30/(15x)]=4(1/2)
30(15x+15+x)/(15^{2}x^{2}) = 9/2
30(30)/225x^{2} =9/2
200 = 225 – x^{2}
X^{2} = 25
X=5km/h
Hence, speed of stream= 5 km/h

Question 3 of 5
3. Question
Two trains, one is of 121 m in length at the speed of 90 km/h and the other is of 99 m n length at the speed of 32 km/h are running in opposite directions. In how much time will they be completely clear from each other from the moment they meet ?
Correct
Ans: b
Total length of train= 121+ 99= 220 m
Total speed of trains=(40 + 32 ) km/h= 72 km/h
ie.72 x(5/18)ms = 20 m/s
∴Time = (Distance/Speed) = 220/20 = 11s
Incorrect
Ans: b
Total length of train= 121+ 99= 220 m
Total speed of trains=(40 + 32 ) km/h= 72 km/h
ie.72 x(5/18)ms = 20 m/s
∴Time = (Distance/Speed) = 220/20 = 11s

Question 4 of 5
4. Question
Three athletes run a 4 km race. Their speeds are in the ratio 16: 15:11. When the winner wins the race, then the distance between the athlete in the second position to the athlete in the third position is
Correct
Ans: a
Ratio of speeds are 16: 15:11.
Let speed of winner athletic be 16x km/h.
Similarly, second and third position of speed of athletic is 15x and
11x, respectively.
Total distance travelled by winner is 4 km.
Time= (4/16x)h
Distance travelled by second athletic in (4/16x)h
= (4/16x) x 15x = 15/4 km
Similarly, distance travelled by third athletic in
(4/16)h = (4/16x) x 11x = 11/4 km
∴Difference between their distances= [(15/4)(11/4)]km
=1km = 1000m
Incorrect
Ans: a
Ratio of speeds are 16: 15:11.
Let speed of winner athletic be 16x km/h.
Similarly, second and third position of speed of athletic is 15x and
11x, respectively.
Total distance travelled by winner is 4 km.
Time= (4/16x)h
Distance travelled by second athletic in (4/16x)h
= (4/16x) x 15x = 15/4 km
Similarly, distance travelled by third athletic in
(4/16)h = (4/16x) x 11x = 11/4 km
∴Difference between their distances= [(15/4)(11/4)]km
=1km = 1000m

Question 5 of 5
5. Question
A man rows downstream 32 km and 14 km upstream and he takes 6 h to cover each distance. What is the speed of the current?
Correct
Ans: C
Let speed of a boat in still water be x and speed of the stream be y km/h.
Then, speed of the boat downstream = (x+ y) km/h
and speed of the boat upstream = (x y) km/h
According to the question,
32/(x+y) = 6 [because speed = (distance/time)
And[ (14)/xy] =6
6x + 6y =32 ………………………………………(1)
And 6x 6y = 14 ……………………………………….(2)
On adding equation 1 and 2 we get
12x = 46⇒x = 46/12 = 23/6
On putting x = 23/6 in Eq. (1), we get
6 x(23/6)+6y =32
6y = 3223
Y=9/6
Y =1.5 km/h
Incorrect
Ans: C
Let speed of a boat in still water be x and speed of the stream be y km/h.
Then, speed of the boat downstream = (x+ y) km/h
and speed of the boat upstream = (x y) km/h
According to the question,
32/(x+y) = 6 [because speed = (distance/time)
And[ (14)/xy] =6
6x + 6y =32 ………………………………………(1)
And 6x 6y = 14 ……………………………………….(2)
On adding equation 1 and 2 we get
12x = 46⇒x = 46/12 = 23/6
On putting x = 23/6 in Eq. (1), we get
6 x(23/6)+6y =32
6y = 3223
Y=9/6
Y =1.5 km/h
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