IMO Practice Test — Ratios & Proportions (Advanced)
6 Questions • 25 min • Olympiad level
25:00
Question 1 of 6
hard
(x+2)/5 = 8/4. Find x.
6
8
10
12
Explanation: 4(x+2) = 40 => 4x + 8 = 40 => 4x = 32 => x = 8
Question 2 of 6
hard
A shopkeeper marks items 40% above cost, then gives a 20% discount. What is the final profit or loss %?
12% profit
12% loss
20% profit
8% profit
Explanation: Let cost=100. Marked=140. Discount=140 x 0.20=28. Selling=112. Profit=12%.
Question 3 of 6
hard
The ratio of boys to girls is 5:7. If there are 60 more girls than boys, how many total students?
240
300
360
420
Explanation: Let boys=5k, girls=7k. 7k-5k=60 => 2k=60 => k=30. Total=12k=360.
Question 4 of 6
hard
A map has scale 1:50,000. Two towns are 8 cm apart. What is the actual distance in km?
0.4 km
4 km
40 km
400 km
Explanation: 8 cm x 50,000 = 400,000 cm = 4,000 m = 4 km
Question 5 of 6
hard
A number increased by 20% gives 72. What is the original number?
57.6
60
86.4
90
Explanation: 1.20 x Original = 72 => Original = 72 / 1.20 = 60
Question 6 of 6
hard
If a/b = 3/4 and b/c = 2/5, find a:c.
3:10
3:20
6:20
6:10
Explanation: Multiply: (a/b) x (b/c) = a/c = (3/4) x (2/5) = 6/20 = 3/10, so a:c = 3:10