IBA Mathematics MCQs

Total work is proportional to workers × hours × days.
So days = 8 × 6 × 15 ÷ (12 × 5) = 12.

Twenty-four workers complete 1/4 in 10 days, so the remaining 3/4 needs 30 equivalent days at the same workforce.
Only 20 days remain, requiring 36 workers, so 12 extra are needed.

In four days, each works twice.
Completed work is 2/15 + 2/20 = 4/30 + 3/30 = 7/30.

Let B's rate be 1 unit and A's 3 units, total 4 units.
A alone takes 8 × 4/3 = 32/3 days.

The machine produces 60/5 = 12 units per hour.
In 8 hours it produces 12 × 8 = 96 units.

If 40% takes 12 days, 10% takes 3 days.
The remaining 60% takes 18 days.

The leak rate is 1/9 - 1/12 = 1/36 tank per hour.
Thus, the leak alone empties the tank in 36 hours.

Speed equals distance divided by time.
Thus, 180 ÷ 3 = 60 km/h.

Distance equals speed multiplied by time.
Thus, 72 × 2.5 = 180 km.

To convert km/h to m/s, multiply by 5/18.
Thus, 54 × 5/18 = 15 m/s.

To convert m/s to km/h, multiply by 18/5.
Thus, 20 × 18/5 = 72 km/h.

Time equals distance divided by speed.
Thus, 12 ÷ 4 = 3 hours.