Time Gain/Loss&Speed Problems

Time Gain/Loss & Speed by Minute and Hour Hands of Clocks in TCS Solved Q's:


Question 1

Priya was presented with new brand watch, as marriage anniversary gift by her husband. She observed, that the two hands of the new watch coincide every 64 minutes. She was trying to calculate, how many minutes the watch will lose per day. Can you guide Priya?

(a)32 8/11 (b)36 5/11 (c) 90 minutes (d) 96 minutes

Answer : a)32 8/11

Solution:
55 min spaces are gained by minute hand (with respect to hour hand) in 60 min. (In 60 minutes, hour hand will move 5 spaces while the minute hand will move 60 spaces. In effect the space gain of minute hand with respect to hour hand will be 60 - 5 = 55 minutes.)
In 60 min it will gain ,
60/55 x60 =65 5/11 min.
But minute hand of Priya's watch gains only 64 minutes (it is slow than normal)
Actual loss=65 5/11 -64 =1 5/11 = 16/11min
In 64 min. the loss is 16/11 min
In 24 hours the loss is = (16/11 x1/64 x24 x60)min =32 8/11 minutes.

Question 2

It was 4’o clock in the evening. Shilu was staring at the new watch that was presented by her Dad two day's ago. She was trying to measure the exact time between 4 and 5’o clock during which the hands of the watch point in opposite directions forming a straight line. What would be that time?

(a) 45 minutes past 4 (b)40 minutes past 4 (c) 50 4/11 minutes past 4
(d)54 6/11 minutes past 4.

Answer : d)54 6/11 minutes past 4.

Solution:
At 4’o clock the hands are 20 minutes apart.To form a straight line in opposite direction the hands must be in 30 minutes apart. To accomplish this the minute hand have to close up the 20 minutes separation and after crossing the hour hand it has to gain 30 minute separation. In total minute hand will have to gain 20 + 30 = 50 minutes spaces apart.
55 min spaces are gained in 60 min. (In 60 minutes, hour hand will move 5 spaces while the minute hand will move 60 spaces. In effect the space gain of minute hand with respect to hour hand will be 60 - 5 = 55 minutes.)
50 min spaces can be gained in 60/55 x50 = 54 6/11 minutes.
Hence the answer is 54 6/11 minutes past 4

Question 3

The famous church in the city of Kumbakonnam has a big clock tower and is said to be over 300 years old. Every Monday 10.00 A M the clock is set by Antony, doing service in the church. The Clock loses 6 mins every hour. What will be the actual time when the faulty clock shows 3 P.M on Friday?

(a) 4 A.M (b) 3.16 P.M. (c) 4.54 A.M. (d) 3 A.M

Answer : c) 4.54 A.M

Solution:
Total hours from Monday 10.00 AM to Friday 3.00 PM =101 HOURS
The clock loses 6 minutes every hour. In 101 hours it will lose 101 x 6 =606 minutes. ie 10 hours 06 minutes.
To find the actual time, calculate 10 hours 6 min backwards from Friday 3.00 PM which is 4 .54 AM
Hence the actual time would be 4 .54 AM when clock shows 3.00 PM on Friday.


Question 4

Suresh Raina and Gautam Gambhir after a scintillating IPL match decide to travel by cycle to their respective villages. Both of them start their journey travelling in opposite directions. Each of their speeds is 6 miles per hour. When they are at a distance of 50 miles, a housefly starts flying from Suresh Raina's cycle towards Gautam Gambhir at a relative speed of 17 miles per hour with respect to Raina's speed. What will be the time taken by housefly to reach Gambhir?

(a)15 hours (b)10 hours (c) 50 hours (d)25 hours

Answer : b)10 hours

Solution:
Since Raina and Gambhir are travelling in opposite directions, Gambhir's Relative speed with respect to Raina's = Speed of Raina + Speed of Gambhir = 6 + 6 = 12 miles per hour.
Now housefly starts from Raina's cycle and travels towards Gambhir's cycle at 17 miles per hour.
Relative speed of housefly with respect to Gambhir = Speed of housefly with respect to Raina - Speed of Gambhir with respect to Raina = 17 - 12 = 5 miles per hour
Time taken for housefly to reach Gambhir = Distance to catch up / Relative speed of housefly with respect to Gambhir = 50/5 = 10 hours.

Question5

Pinky and Ponky decided to have a car race. Initially Pinky was 20 miles behind Ponky’s car. Both of them took the race in the same direction along the same route. Pinky was travelling at a constant speed of 68 miles per hour, while Ponky was travelling at a constant speed of 60 miles per hour. How many hours will it take for Pinky to overtake and drive 8 miles ahead of Ponky?

(a)1.7 hours (b)2.0 hours (c)2.5 hours (d)3.0 hours (e) 3.5 hours

Answer : e) 3.5 hours

Solution:
It is to be understood from the problem, that Pinky has to travel 20 miles first to catch up Ponky. Then, he has to travel an additional 8 miles to be ahead of Ponky. Pinky has to travel a total of 28 extra miles relative to Ponky’s car.
Relative Speed of Pinky with respect to Ponky = 68 - 60 = 8 miles per hour.
Time taken for Pinky to cover 28 extra miles compared to that of Ponky = Extra Distance / Relative Speed of Pinky with respect to Ponky = 28/8 = 3.5 hours.

Question 6

Eveson was working for a multinational company. The pressure of work in the company was too heavy due to seasonal sales. Eveson decided to go weekend trip with his wife for relaxation. Husband and wife decided that the proposed trip should not exceed 8 hours driving in a day. They decided to maintain the average Speed of forward journey to 40 mph. Due to traffic on Sundays the return journey average speed can only be at 30 mph. How far the couple can select a picnic spot?

(a)142 Miles (b)200 Miles (c)137 Miles (d)220 Miles

Answer : c)137 Miles

Solution:
If x and y are the speeds corresponding to forward and return journeys, then average speed of the entire journey can be found using the formula : 2xy / x+y
In our case the rate for onward journey is given as 40 mph and rate for return journey is given as 30 mph
Hence average speed = 2x40x30 / 40+30 = 2400 / 70 = 240 / 7 mph
Total Travel Time is 8 hours. So total distance the couple can plan = Average Speed x Affordable Total Time = 240 / 7 x 8 =1920 / 7 = 274 miles (approximately)
Since 274 miles should be the total distance that can be covered including forward and return journeys, the picnic spot has to be at 274 / 2 = 137 miles approximately.

Question 7

Rambabu is driving a Honda Unicorn Power bike at 80 km per hour. However being sugar patient, Rambabu could not travel continuously. He takes small breaks each of 2 minutes for every 15 minute of his drive. How much distance Rambabu will cover in 90 minutes?

a)118Km b)89Km c)112Km d) 104km

Answer : d) 104km

Solution:
For every 15 minutes he takes a rest for 2 minute.
Hence for 90 minutes of drive he would require 12 minutes of rest. In effect he will be traveling for 90 - 12 = 78 minutes.
For 60 minutes he covers 80 Km.
For 1 minute he would cover 80/60 Km.
For 78 minutes he would cover (80/60)78 = 104 Km