KCSE 2025 Maths P1 Q2 — Ratio: Changing an Hourly Rate
Published
The Question
“Baraka earns Ksh 210 per hour working at a supermarket. His employer changed the amount earned per hour in the ratio 8:7. Determine the amount that Baraka would earn in 10 and a half hours at the new rate.”
Read the ratio in the right order
The pay is changed in the ratio 8 to 7. This is written as new to old, so the new rate compares to the old rate as 8 to 7. That means the new rate is the old rate multiplied by 8 over 7. Because 8 is bigger than 7, the pay goes up, which is what we expect for a rate change like this.
Work out the new hourly rate
Substitute the old rate of 210 shillings. It is easier to divide by 7 first: 210 divided by 7 is 30, then multiply by 8 to get 240. So the new rate is 240 shillings per hour.
Dividing before multiplying keeps the numbers small and avoids a large multiplication.
Write the time as an improper fraction
The question asks for 10 and a half hours. Turn this mixed number into a single fraction so it multiplies cleanly. Ten and a half is twenty-one halves.
Multiply the rate by the hours
Total earnings are the new rate times the number of hours. Multiply 240 by twenty-one halves. Half of 240 is 120, then multiply by 21 to get 2,520 shillings.
Final Result
Baraka would earn Ksh 2,520 for 10 and a half hours at the new rate.
Why this method works
Changing a quantity in a given ratio means scaling it by the fraction formed from the two numbers, keeping the order the ratio is stated in. Here the ratio 8:7 is new to old, so multiplying by 8 over 7 stretches the old rate up to the new one. Once the correct rate per hour is found, earnings are simply rate multiplied by time, because pay grows in direct proportion to the number of hours worked.
Reverse it: 240 divided by 8, times 7, returns 210, confirming the ratio was applied correctly; and 240 times 10.5 equals 2,520.