The shopkeeper buys 120 notebooks at ₹40 each.
The shopkeeper sells 120 notebooks at ₹50 each.
Profit is the difference between selling price and cost price.
The shopkeeper's total profit for selling 120 notebooks in a day is ₹1,200.
Let the total distance be \(D\) km. The car travels \(\frac{D}{2}\) km at each speed.
For the first half at 60 km/h:
For the second half at 90 km/h:
Total time for the journey:
Average speed is total distance divided by total time:
The average speed for the entire journey is 72 km/h.
The boat travels 120 km downstream in 6 hours.
The boat travels 120 km upstream in 8 hours.
The speed of boat in still water is the average of downstream and upstream speeds.
The speed of the boat in still water is 17.5 km/h.
[Cyclist 1 completes one lap]
[Cyclist 2 completes one lap]
[The cyclists will meet at the starting point when the time elapsed is a common multiple of both lap times]
[Finding prime factorization: 75 = 3 × 5², 60 = 2² × 3 × 5]
[In 300 seconds, Cyclist 1 completes]
[In 300 seconds, Cyclist 2 completes]
[Both return to the starting point after completing whole laps
Let the distance between A and B be \(d\) km. Time to go from A to B at 4 km/h is \(\frac{d}{4}\) hours, and time to return from B to A at 6 km/h is \(\frac{d}{6}\) hours.
The common denominator of 4 and 6 is 12. Rewrite each fraction with denominator 12.
Combine the fractions on the left side and solve for \(d\).
The distance between A and B is 12 km.
The train travels 240 km in 4 hours, so we divide distance by time.
The speed increases by 20%, so we multiply the original speed by 1.20.
Distance equals speed multiplied by time.
The train will cover 360 km in 5 hours at the new speed.