GK 2019 Q22
22. When Ria and Flora compared the amounts of money in their savings accounts, they found that their savings were in the ratio 5 : 3. Then Ria took 160 euros from her savings to buy a tablet. The ratio of their savings then changed to 3 : 5. How many euros did Ria have before buying the tablet?
- A 192
- B 200
- C 250
- D 400
- E 420
Grey Kangaroo 2019, Question 22. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 250
The original ratio of the amounts of money in Ria’s and Flora’s savings accounts was 5 : 3 = 25 : 15. After Ria withdrew 160 euros, the ratio changed to 3 : 5 = 9 : 15. Since Flora’s savings have not changed, the 160 euros Ria withdrew represented \(\tfrac{(25 - 9)}{25} = \tfrac{16}{25}\) of her original savings. Therefore 10 euros represented \(\tfrac{1}{25}\) of her original savings and hence she originally had 250 euros.
Solution © UK Mathematics Trust, from the GK 2019 solutions.