KJSEA 2025 Maths Q4 — Fractions of Time (Extra Time Calculation)

KJSEA 2025 Grade 9 Numbers

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The Question

“Kamal planned to use one fifth of an hour to plant each seedling, but he actually took one quarter of an hour for each. There were 70 seedlings. Which calculation gives the extra time he used altogether?”

1

Understand what 'extra time' means

Extra time is how much longer each seedling actually took compared with the plan. The actual time per seedling was a quarter of an hour, and the planned time was a fifth of an hour. So the extra time for one seedling is the actual time minus the planned time.

extra per seedling=14−15\text{extra per seedling} = \frac{1}{4} - \frac{1}{5}

Subtract the smaller planned fraction from the larger actual fraction, because a quarter of an hour is longer than a fifth of an hour.

2

Confirm which fraction is larger

It helps to see that a quarter really is bigger than a fifth, so the subtraction is done the right way round. Writing both with a common denominator of twenty makes this clear and shows the extra time is a small positive amount.

14=520,15=420\frac{1}{4} = \frac{5}{20}, \quad \frac{1}{5} = \frac{4}{20}
14−15=520−420=120\frac{1}{4} - \frac{1}{5} = \frac{5}{20} - \frac{4}{20} = \frac{1}{20}
3

Scale up for all 70 seedlings

That extra time is for just one seedling. Since Kamal planted seventy seedlings and each one carried the same extra amount, multiply the extra time per seedling by 70 to get the total extra time.

(14−15)×70\left( \frac{1}{4} - \frac{1}{5} \right) \times 70
4

Pick the matching option

The calculation that represents the total extra time is the difference of the two fractions, all multiplied by 70. This matches option D. Option A is wrong because it adds the times instead of comparing them, and option C is wrong because it reverses the subtraction, which would give a negative result.

(14−15)×70(option D)\left( \frac{1}{4} - \frac{1}{5} \right) \times 70 \quad \text{(option D)}

Final Result

The correct calculation is (1/4 − 1/5) × 70, which is option D.

Why this method works

Extra time is a comparison, not a total, so you subtract the planned time from the actual time rather than adding them. Doing the subtraction in the order actual minus planned keeps the result positive, since a quarter of an hour is genuinely longer than a fifth. Because every one of the 70 seedlings carried exactly the same extra amount, multiplying the per-seedling difference by 70 correctly totals the extra time for the whole job.

✓

Working it out fully: (1/4 − 1/5) × 70 = (1/20) × 70 = 3.5 hours of extra time, a sensible positive amount.