IBA Mathematics MCQs

Relative speed is 66 km/h = 55/3 m/s.
Length = speed × time = 55/3 × 18 = 330 meters.

Downstream speed equals still-water speed plus stream speed.
Thus, 12 + 3 = 15 km/h.

Upstream speed equals still-water speed minus stream speed.
Thus, 10 - 2 = 8 km/h.

Downstream speed is 15 km/h and upstream speed is 10 km/h.
Still-water speed is their average: 12.5 km/h.

In the same time, the faster runner covers 1,000 m while the slower covers 900 m.
Their speed ratio is therefore 1,000:900 = 10:9.

Time is inversely proportional to speed.
The decrease is 1 - 50/60 = 1/6 = 16 2/3%.

Let total distance be 3d; time is d/30 + 2d/60 = d/15.
Average speed is 3d ÷ (d/15) = 45 km/h.

Travel time is 210 ÷ 70 = 3 hours.
Three hours after 8:00 a.m. is 11:00 a.m.

Their closing speed is 20 + 25 = 45 km/h.
Time = 90 ÷ 45 = 2 hours.

The remaining part is 3/4 of the tank.
At 8 hours per full tank, 3/4 takes 6 hours.

Daily wage equals total earnings divided by days worked.
Thus, 3,600 ÷ 12 = Rs. 300.

A's share is 3 out of 8 total parts.
Thus, A receives 3/8 × 4,800 = Rs. 1,800.