A toy shop had teddy bears and robots in the ratio 5 : 6 at first. The shop sold 20 teddy bears and received 40 more robots. After this, the ratio of the number of teddy bears to the number of robots became 1 : 2.
- Find the number of teddy bears at first.
- Find the number of robots at first.
Need a hint?
Write the first ratio in units, then write the after-sale numbers as units minus or plus the given change. Use the new ratio 1 : 2 to form an equation.
Worked answer
- Let one unit be u. At first, teddy bears = 5u and robots = 6u.
- After the sale, teddy bears = 5u − 20 and robots = 6u + 40.
- The new ratio is 1 : 2, so robots = 2 × teddy bears: 6u + 40 = 2(5u − 20).
- 6u + 40 = 10u − 40, so 4u = 80 and u = 20.
- Teddy bears at first = 5 × 20 = 100.
- Robots at first = 6 × 20 = 120.
Answer: 120 robots
The mistake this question tests
Habit
Stopped at one part in ratio
Pupils often apply the new ratio to the first numbers instead of the numbers after the sale, which skips the 20 sold and the 40 received.
How to fix it at home →More PSLE ratio questions
Short answer · 2m
The ratio of boys to girls in a class is 3 : 5
See the answer →Structured · 3mPriya and Marcus had some stickers each
See the answer →MCQ · 2mPoints P, Q, R, S and T lie in that order on a straight path
See the answer →Short answer · 2mOn Arun's town map, 3 cm represents 15 km
See the answer →Structured · 4mA box contains red and blue beads
See the answer →MCQ · 2mIn a park, the ratio of the number of trees in Garden P to the number of trees in Garden Q is 3 : 5
See the answer →Practise PSLE ratio until the mistakes stop.
Three PSLE questions, free, no sign-up. You’ll see exactly where the marks went. Then 7 days of everything for S$4.99.