Question
In an AP, S₅ = 75 and S₇ = 119, where S_n is sum of
first n terms. Find the 10th term.Solution
ATQ,
S_n = n/2[2a + (n−1)d]. S₅ = 5/2(2a + 4d) = 75 ⇒ 2a + 4d = 30. S₇ = 7/2(2a + 6d) = 119 ⇒ 2a + 6d = 34. Subtract: 2d = 4 ⇒ d = 2. Then 2a + 8 = 30 ⇒ a = 11. 10th term = a + 9d = 11 + 18 = 29.
A ferry takes 75 minutes to row to place B from another place A along the stream. The distance between place A and place B is 37.5 km. If the speed of t...
In a 250-metre race, ‘A’ beats ‘B’ by 16 seconds or 80 metres. Find the time taken by ‘B’ to finish the race.
A car's speed is 20% faster than that of a bike. The car takes 30 minutes longer than the bike to cover 120 km, while the bike covers 80 km. Find the ti...
A bus initially traveling at a speed of 55 km/hr increased its speed by 12 km/hr after ‘t’ hours and then traveled for (t + 6) hours more. If the bu...
A train travels from station ‘P’ to station ‘Q’ at a constant speed. If its speed was increased by 20 km/h, it would have taken 1 hour less to c...
- A sphere has a diameter of 35 cm. Find its total surface area.
A motorcycle begins its journey at point X, traveling at a constant speed of 85 km/h. Meanwhile, a car starts at point X with a speed of 60 km/h and acc...
A man walks at a speed of 5 km/h. How much time will he take to cover 12.5 km?
A motor-cycle covers 160 km with a speed of 70 km/hr. find the speed of the motor-cycle for the next 170 km journey so that the average speed of the who...
- A person walks at 5 km/h and needs to reach home in 2 hours. After walking half the distance, they rest for 20 minutes. What must be their speed for the re...
