Alliance Form 3 P1 Q17 — Ratio, Trips & Profit (Farmer's Maize)

KCSE (Form 3) Form 3 Numbers

Published

The Question

“A farmer has 540 bags of maize, each with a mass of 112 kg. After drying, the mass of each bag decreases in the ratio 15 to 16. (a) Find the total mass of maize lost after drying. (b) The dried maize is repacked into 90 kg bags and transported by a lorry that carries 120 bags per trip. Find the number of trips the lorry makes. (c) The trader buys the 90 kg bags at 1,500 shillings each and pays 2,500 shillings transport per trip. Find the selling price per bag that gives a 26% profit.”

1

Find the dried mass of one bag

The mass decreasing in the ratio 15 to 16 means the dried mass is fifteen sixteenths of the original mass. Multiply the original 112 kg by fifteen over sixteen to get the new mass of a single bag. This works because a ratio of old to new here compares the smaller dried mass against the larger fresh mass.

112×1516=105 kg112 \times \frac{15}{16} = 105 \text{ kg}
2

Work out the total mass lost

Each bag drops from 112 kg to 105 kg, so it loses 7 kg. To find the mass lost across the whole harvest, multiply the loss per bag by the 540 bags. The loss is the same for every bag, so simple multiplication gives the total.

112−105=7 kg per bag112 - 105 = 7 \text{ kg per bag}
7×540=3,780 kg7 \times 540 = 3{,}780 \text{ kg}
3

Count the 90 kg bags after repacking

The dried maize is repacked, so first find the total dried mass by multiplying the dried mass of one bag by the number of bags. Dividing that total by 90 kg tells you how many new bags are filled.

105×540=56,700 kg105 \times 540 = 56{,}700 \text{ kg}
56,700÷90=630 bags56{,}700 \div 90 = 630 \text{ bags}
4

Find the number of lorry trips

The lorry carries 120 bags each trip, so divide the 630 bags by 120. This gives 5.25, but a lorry cannot make a quarter of a trip. Since even the leftover bags must still be carried, you always round up to the next whole trip.

630÷120=5.25⇒6 trips630 \div 120 = 5.25 \Rightarrow 6 \text{ trips}
5

Add up the total cost

Cost comes from two sources: buying the bags and paying for transport. Multiply 630 bags by the buying price of 1,500 shillings, then add the transport of 2,500 shillings for each of the six trips. Their sum is the total cost the trader must recover before making any profit.

630×1,500=945,000630 \times 1{,}500 = 945{,}000
2,500×6=15,0002{,}500 \times 6 = 15{,}000
945,000+15,000=960,000 shillings945{,}000 + 15{,}000 = 960{,}000 \text{ shillings}
6

Apply the 26% profit and share per bag

A 26% profit means the total selling amount is 126% of the cost, so multiply the total cost by 1.26. Dividing that total revenue by the 630 bags gives the price each bag must be sold at.

960,000×1.26=1,209,600960{,}000 \times 1.26 = 1{,}209{,}600
1,209,600÷630=1,920 shillings1{,}209{,}600 \div 630 = 1{,}920 \text{ shillings}

Final Result

The total mass of maize lost after drying is 3,780 kg, the lorry makes 6 trips, and each bag must be sold at 1,920 shillings to earn a 26% profit.

Why this method works

The problem chains three ideas together. The drying ratio 15 to 16 is a scale factor: because the dried mass is the smaller quantity, it is fifteen sixteenths of the fresh mass, so multiplying by that fraction shrinks each bag correctly. The trip count rounds up rather than off because transport is about physically moving every last bag, so any remainder still needs a full journey. Finally, adding a 26% profit is the same as multiplying the recovered cost by 1.26, since 100% represents breaking even and the extra 26% is the gain the trader wants.

✓

Reverse-check part (c): 1,920 times 630 equals 1,209,600, and 1,209,600 divided by 960,000 equals 1.26, confirming exactly a 26% profit.