ECAT Mathematics MCQs

Doubling means interest equal to the principal is earned in 8 years.
Tripling requires interest equal to twice the principal, so it takes 16 years.

Worker-days remain constant for the same job.
Thus, 15 × 20 ÷ 12 = 25 workers.

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.

One-year compound amount is principal plus 12% interest.
Thus, 20,000 × 1.12 = Rs. 22,400.

Twice the efficiency means twice the daily work rate.
Therefore, A takes half of 18 days, which is 9 days.

Profit is shared in the ratio of investments, 3:5.
B receives 5/8 of Rs. 16,000 = Rs. 10,000.

In 5 days, A completes 5/20 = 1/4 of the job.
Therefore, 3/4 remains.

Capital-time products are 40,000 × 12 and 60,000 × 8.
Both equal 480,000, so the ratio is 1:1.

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

A's capital-time is 2 × 6 + 4 × 6 = 36 units.
B's is 3 × 12 = 36 units, so profits are equal.

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

A 20% profit gives a selling price of Rs. 960.
Since this is 80% of marked price, marked price = 960/0.8 = Rs. 1,200.