1. Nishu is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the speed of the train?
A. 35 kmph
B. 54 kmph
C. 62 kmph
D. 70 kmph
Answer: Option B
Explanation:
Let the length of the train be x metres.
Then, the train covers x metres in 8 seconds (train is actually covering itself because length of man is very less compartable to train)and (x + 180) metres in 20 seconds.
equate speed in both case,s = [latex]\frac{d}{t}[/latex]
∴ [latex]\frac{x}{8}[/latex] = [latex]\frac{x + 180}{20}[/latex]
⇔ 20x = 8([latex]\frac{x + 180}{20}[/latex]) ⇔ x = 120.
∴ Length of the train = 120 m.
Speed of the train = [latex]\frac{120}{8}[/latex]m/sec (convert to km/hr i.e x [latex]\frac{18}{5}[/latex])
=[latex]\frac{120}{8}[/latex] x [latex]\frac{18}{5}[/latex] kmph = 54 kmph.
2. Two train travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. Then length of the faster train is:
A. 120 m
B. 140 m
C. 160 m
D. 180 m
Answer: Option D
Explanation:
When OPP. direction-PLUS
Relative speed = (36 + 45) km/hr
= [81 x [latex]\frac{5}{18}[/latex]] m/sec = [latex]\frac{45}{2}[/latex] m/sec.
Length of train = [latex]\frac{45}{2}[/latex] x 8 m = 180 m.
3. A can do a piece of work in 60days working 14 hours. B has the same efficiency as of A. A and B started working together. A works 5,6,7 and 8 hours respectively on first four days and repeats the cycle again. Then B has to work how many hours daily if they together completed the work in 80 days?
A. 1 Hour
B. 2 Hours
C. 3 Hours
D. 4 Hours
Answer: Option D
Explanation:
[latex]\frac{20*(5 + 6 + 7 + 8 + 4x)}{840}[/latex] = 1
x = 4 hours
4. Sruthi, Swetha and Swati together can cut 216 Apples of the same size in 3 hours. Number of Apples cut by Sruthi in 9 hours is same as the number of Apples cut by Swati in 7 hours. In one hour, Swati can cut as many Apples more than Swetha as Swetha can cut more than Sruthi.Then the number of Apples cut by Swetha in one hour?
Answer: Option B
Explanation:
U + v + W = 72
9U = 7W
W - V = V-U
V = 24
5. A labourer was appointed by a contractor on the condition he would be paid Rs 150 for each day of his work but would be, fined a the rate of Rs 30 per day for his absent. After 20 days, the contractor paid the laborer’s 2820. Find the number of days he worked:
A. 13 days
B. 19 days
C. 5 days
D. 12 days
Answer: Option B
Explanation:
Let the required number of days = x days
So, 150x -(20 - x)30 = 2820
x = 19 days