Higher June 2025 Paper 2 Q6
6 Pau, Sam and Tia share £240 in the ratios \(3 : 4 : 5\)
Sam and Tia each give £10 of their share to Pau.
Work out the ratios of the amounts of money that Pau, Sam and Tia now have.
Give your answer in its simplest form.
(4)
| Scheme | Marks |
|---|---|
240 ÷ (3 + 4 + 5) (= 20) or \(240 \times \dfrac{3}{3 + 4 + 5}(= 60)\) oe or \(240 \times \dfrac{4}{3 + 4 + 5}(= 80)\) oe or \(240 \times \dfrac{5}{3 + 4 + 5}(= 100)\) oe | M1 |
| For two of (Pau:) 3 × “20” + 10 + 10 ( = 80) or “60” + 10 + 10 ( = 80) (Sam:) 4 × “20” – 10 ( = 70) or “80” – 10 ( = 70) (Tia:) 5 × “20” – 10 ( = 90) or “100” – 10 ( = 90) | M1 |
| 80, 70 and 90 or eg 9 : 7 : 8 oe or eg 4 : 3.5 : 4.5 oe | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: 8 : 7 : 9 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a correct method to find the value of one share
NB (240 ÷ 3 =) 80, (240 ÷ 4 =) 60 and (240 ÷ 5 =) 48 scores M0
M1: for the correct values for 2 of the people after S and T give P £10
M1: for all 3 of 80, 70, and 90 correct (ignore units)
or
for the correct values for the final ratio in the wrong order (ignore units)
or
for the correct values for the final ratio unsimplified (ignore units)
A1: other orders are acceptable if labelled correctly