2025 CGSS PRELIMS P2 Q8

A factory produces bowls in two sizes, small size and large size.

1. It is found that \(x\) large bowls can be produced in a minute. Write down an expression in terms of \(x\), the time taken to produce 1 large bowl, in seconds.[1]
2. 4 more small bowls can be produced in a minute, compared to the large bowls. Write down an expression in terms of \(x\), the time taken to produce 1 small bowl, in seconds.[1]
3. Given that it takes 2.5 seconds longer to produce a large bowl than a small bowl, form an equation in \(x\) and show that it reduces to \(x^2+4x-96=0\).[2]
4. Solve the equation \(x^2+4x-96=0\).[2]
5. Hence find the time taken to produce 3500 small bowls. Give your answer in hours and minutes, correct to the nearest minute.[2]
6. The factory sells each small bowl at $0.35 and each large bowl at $0.50. Explain, with clear workings, why it is more profitable for the factory to produce only small bowls than only large bowls.[3]