1MA0 Foundation November 2016 Paper 2 Q26
26 There are 165 counters in a bag.
Each counter is either black or white.
There are twice as many black counters as white counters in the bag.
Martine takes 40% of the black counters from the bag.
Work out the ratio of the number of black counters to the number of white counters now in the bag.
Give your ratio in its simplest form. (4)
| Answer | Mark | Notes |
|---|---|---|
| 6 : 5 | 4 | M1 for \(\frac{2}{3} \times 165\) oe (= 110) [black counters] M1 (dep M1) for \(\frac{40}{100} \times \text{``}110\text{''}\) oe (= 44) [where 110 is their black counters] M1 (dep M2) for \((110 - \text{``}44\text{''}) : 55\) or 66 : 55 or a reversed ratio A1 cao OR M1 for 2 : 1 M1 for \(2 \times \text{``}1 - 0.4\text{''}\) or 1.2 M1 (dep M2) for “1.2” : 1 A1 cao OR M1 for correct method to find proportion of black counters left in the bag eg \(\frac{60}{100} \times \frac{2}{3}\ \left(= \frac{120}{300}\right)\) M1 for correct method to find proportion of white counters in the bag ie \(\frac{1}{3}\) oe M1 (dep M2) for correct method to find ratio after eg \(\text{``}\frac{120}{300}\text{''} : \text{``}\frac{1}{3}\text{''}\) A1 cao |