Question
A man travels from town A to town B at 45 km/h and
returns from B to A at 30 km/h. If the distance between A and B is 120 km, find the total time taken for the round trip and his average speed.Solution
ATQ, Time A→B = 120 / 45 = 8/3 hours (2 h 40 min) Time B→A = 120 / 30 = 4 hours Total time = 8/3 + 4 = 8/3 + 12/3 = 20/3 hours (6 h 40 min) Total distance = 120 + 120 = 240 km Average speed = Total distance / Total time = 240 ÷ (20/3) = 240 × 3/20 = 36 km/h Answer: Total time = 6 h 40 min; average speed = 36 km/h.
Find the value of 3/4 cot² 30° + cos² 30°-3cosec²60° + tan² 60°.

If √y + (1/√y) = 10, then find the value of y + (1/y).
x + y = 4, xy = 2, y + z = 5, yz = 3, z + x = 6 and xz =4, then find the value of x 3  + y 3  + z 3  – 3xyz.
...if 2x +3y =7 and 2x+2 -3y+2 =7, then find the value of x and y.
If x + y + z = 6, and x3 + y3 + z3 = 36, xyz = 6 then find (xy +yz + zx)?
- If (510 – 486 + 240) ÷ 8 + √2500 = x, then {(x/2) + 18} = ?
If a² + c² + 17 = 2(a - 8b - 2c²), then what is the value of (a³ + b³ + c³)?
The area of â–³ ABC is 44 cm2 . If D is the midpoint of BC and E is the midpoint of AB, then the area of â–³ BDE isÂ
- If n = 1 + √2, then find the value of (n + 1/n)².