4.3 Everyday Word Problems: Money, Time, Ages, Averages & Units

4.3 Everyday Word Problems: Money, Time, Ages, Averages & Units

Many quantitative questions on a recruit aptitude paper are not labelled "fractions" or "algebra". They are short stories about pay, duty rosters, journeys, ages, stores and measurements. The arithmetic is usually simple. The difficulty lies in reading the story correctly and turning it into the right calculation. This section gives you a method for doing that and drills the everyday situations that appear most often: money in cedis, time on the 24-hour clock, age puzzles, averages, combined rates and unit conversions.

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The Four-Step Method

1. Read for the question. Find the exact quantity asked for (the change? the arrival time? the original price?). Underline it.
2. Define and record. Write each given number with its unit, and name any unknown with a letter.
3. Translate and solve. Turn the words into operations or an equation, then calculate.
4. Check the answer against the story. Is it in the right unit? Is it sensible? (A recruit cannot be 3 years old; change cannot exceed the note handed over.)

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Money in Cedis and Pesewas

Ghana's currency is the cedi (GH₵), divided into 100 pesewas (Gp). So GH₵3.45 is 3 cedis and 45 pesewas, or 345 pesewas.

Worked example: change. A soldier buys 3 pairs of socks at GH₵18.50 each and a belt for GH₵45.00, paying with a GH₵200 note.

• Socks: $3 \times 18.50 = 55.50$
• Total spent: $55.50 + 45.00 = 100.50$
• Change: $200.00 - 100.50 = 99.50$

The change is GH₵99.50.

Worked example: best value. A 5 kg bag of rice costs GH₵140 and a 25 kg bag costs GH₵650. Compare the unit price (price per kilogram):

• Small bag: $140 \div 5 = 28$ cedis per kg
• Large bag: $650 \div 25 = 26$ cedis per kg

The large bag is cheaper by GH₵2 per kilogram.

Worked example: working backwards from a percentage. After a 12% increase, an allowance is GH₵1,568. What was it before?

$$\text{Original} = \frac{1568}{1.12} = 1400$$

The original allowance was GH₵1,400. A common trap is to subtract 12% of GH₵1,568, which gives the wrong answer of about GH₵1,380.

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Time and the 24-Hour Clock

The Armed Forces write times on the 24-hour clock with four digits, often followed by "hours".

Durations that cross midnight. A guard shift runs from 2215 to 0630.

• From 2215 to midnight: 1 hour 45 minutes
• From midnight to 0630: 6 hours 30 minutes
• Total: 8 hours 15 minutes

Do not subtract the clock times directly (0630 − 2215 gives nonsense). Always split the interval at midnight.

Arrival times. A convoy leaves at 0940 and travels 195 km at an average 60 km/h.

$$t = \frac{195}{60} = 3.25 \text{ hours} = 3 \text{ h } 15 \text{ min}$$

It arrives at 0940 + 3 h 15 min = 1255.

Calendars. April, June, September and November have 30 days; February has 28 days, or 29 in a leap year; every other month has 31. A year divisible by 4 is a leap year, except century years that are not divisible by 400 (2000 was a leap year; 2100 will not be). Because 7 days make a week, move forward by the remainder after dividing by 7. If 1 January 2027 is a Friday, then 31 days later, 1 February 2027, is $31 = 4 \times 7 + 3$, so three days after Friday: Monday.

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Age Problems

Let a letter stand for one person's age now, then write every other age in terms of it. Add the same number of years to everyone for "in ___ years", and subtract for "___ years ago".

Worked example. Ama is three times as old as her son Kojo. In 12 years she will be twice as old as he is. Find their ages now.

• Let Kojo's age be $k$, so Ama's age is $3k$.
• In 12 years: $3k + 12 = 2(k + 12)$
• Expand: $3k + 12 = 2k + 24$, so $k = 12$

Kojo is 12 and Ama is 36. Check: in 12 years they will be 24 and 48, and 48 is twice 24.

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Averages

The mean (average) is the total divided by the number of items, so total = mean × number. Most average questions are solved through totals.

Worked example. Eight recruits have a mean shooting score of 36. When a ninth recruit's score is added, the mean rises to 37. What did the ninth recruit score?

• Old total: $8 \times 36 = 288$
• New total: $9 \times 37 = 333$
• Ninth score: $333 - 288 = 45$

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Filling, Leaking and Combined Rates

When quantities go in and out at the same time, combine the rates first.

Worked example. A 1,200-litre tank already holds 950 litres. A pump adds 40 litres per minute while a leak loses 15 litres per minute. How long until the tank is full?

• Space left: $1200 - 950 = 250$ litres
• Net rate: $40 - 15 = 25$ litres per minute
• Time: $250 \div 25 = 10$ minutes

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Metric Units

Convert everything to the same unit before calculating. For example, a 2.5-litre bottle fills $2500 \div 250 = 10$ cups of 250 mL.

Shapes in stories. A rectangular parade square has a perimeter of 64 m, and its length is three times its width. Then $2(3w + w) = 64$, so $8w = 64$, $w = 8$ m, the length is 24 m and the area is $24 \times 8 = 192$ m².

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Traps to Avoid