Two people A and B start simultaneously from points P and Q towards Q and P respectively. After meeting for the first time, A and B take 8 hours and 18 hours respectively to reach their destination. If A travels at a speed of 96 kmph, find the speed of B.

Two people A and B start simultaneously from points P and Q towards Q and P respectively. After meeting for the first time, A and B take 8 hours and 18 hours respectively to reach their destination. If A travels at a speed of 96 kmph, find the speed of B.
1). 32 kmph
2). 48 kmph
3). 56 kmph
4). 64 kmph

When A and B meet for the first time, both of them have travelled for the same time

As a result, the distance covered by them will be equal to the ratio of their speeds

Let the time taken to meet for the first time be ‘T’ hours from the time of the start

A and B would take (T + 8) and (T + 18) hours respectively to cover the entire distance

⇒ Ratio of the total time taken by A and B = (T + 8) : (T + 18)

If the distance is constant, then the speed is inversely proportional to Time

⇒ Ratio of speeds of A : B = (T + 18) : (T + 8)

Given A’s speed = 96 km/hr

When they meet for the first time, A should have covered (96 × T) kms which is the distance which B will cover in 18 hours

Speed of B = (Distance/Time) = (96 × T)/18 kmph

⇒ Ratio of the speeds of A and B = 96 : (96T/18)

⇒ (T + 18) : (T + 8) = 96 : (96T/18)

⇒ (T + 18) : (T + 8) = 18 : T

⇒ (T + 18) × T = (T + 8) × 18

⇒ T² + 18T = 18T + 144

⇒ T² = 144

⇒ T = 12 hours

Speed of B = (96 × 12)/18 kmph = 64 kmph

∴ Speed of B = 64 kmph

• Point A is 30 metres to the east of point B. Point C is 10 metres to the south of Point A. Point D is 15 metres to the west of Point C. Point E is exactly in the middle of the Points D and F. Points D, E and F lie in a straight line. The length of the lin
• The ratio of the sum of the salaries of A and B to the difference of their salaries is 11 : 1 and the ratio of the sum of the salaries of B and C to the difference of their salaries is also 11 : 1. If A's salary is the highest and C's is the lowest then w
• There are three taps A, B and C in a tank. They can fill the tank in 25 hrs, 20 hrs and 10 hrs respectively. At first all of them are opened simultaneously. Then after 1 hrs, tap C is closed and tap A and B are kept running. After the 4th hour, tap B is a
• In a hotel, the rooms are numbered from 101 to 130 on the first floor, 221 to 260 on the second floor and 306 to 345 on the third floor. In the month of June this year, the room occupancy was 60% on the first floor, 40% on the second floor and 75% on the
• Nidhi received simple interest off Rs. 1200 when invested Rs x at 6% p.a. and Rs y at 5% p.a. for 1 year. Had she invested Rs. x at 3% p.a. and Rs. y at 8% for that year, she would have received simple interest of Rs 1,260. Find the values Rs. x an y.