Mathematics MCQs

If half the work takes 6 days, the full work takes twice as long.
Thus, the total time is 12 days.

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

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

Multiply both sides by 4.
Thus, x = 7 × 4 = 28.

The common difference is 4.
Adding 4 to 19 gives 23.

Their combined rate is 1/12 + 1/18 + 1/36 = 1/6.
Therefore, they finish in 6 days.

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

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

Adding the equations gives 2x = 14, so x = 7.
Substituting into x + y = 10 gives y = 3.

The nth term is a + (n - 1)d.
Thus, 3 + 9 × 4 = 39.

Let B's rate be 2 units and A's rate be 3 units, total 5 units.
If 5 units finish in 6 days, B alone takes 6 × 5/2 = 15 days.

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