IMO Practice Test — Ratio, Proportion and Percentages
6 Questions • 15 min • Olympiad level
15:00
Question 1 of 6
The ratio of copper to zinc in an alloy is 7:3. If the weight of copper is 3.5 kg, find the weight of zinc.
1.0 kg
1.2 kg
1.5 kg
1.8 kg
Explanation: 7 parts = 3.5 kg → 1 part = 0.5 kg; Zinc=3 parts=1.5 kg
Question 2 of 6
A sum of money is divided between A and B in the ratio 5:3. A gets ₹240 more than B. Find the total sum.
₹480
₹720
₹960
₹1200
Explanation: Let A=5x, B=3x; A-B=2x=240 → x=120; Total=8x=₹960
Question 3 of 6
The ages of A and B are in ratio 5:7. Four years later, the ratio will be 3:4. Find A's present age.
16 years
18 years
20 years
22 years
Explanation: A=5x, B=7x; (5x+4)/(7x+4)=3/4; 4(5x+4)=3(7x+4); 20x+16=21x+12; 4=x; A=5×4=20
Question 4 of 6
A map is drawn to a scale of 1:20000. Two cities are 8 cm apart on the map. Find the actual distance in km.
1.2 km
1.4 km
1.6 km
1.8 km
Explanation: 8×20000=160000 cm=1.6 km
Question 5 of 6
If \(A:B = 2:3\), \(B:C = 4:5\), \(C:D = 6:7\), find \(A:D\).
16:35
35:16
8:35
35:8
Explanation: A/B=2/3, B/C=4/5, C/D=6/7; A/D=(2/3)×(4/5)×(6/7)=48/105=16/35 → 16:35
Question 6 of 6
20 workers can complete a task in 12 days. After 4 days, 4 workers left. How many more days will be needed to complete the remaining work?
8 days
9 days
10 days
11 days
Explanation: Total work=20×12=240 man-days; 4 days work=20×4=80 done; Remaining=160; Workers left=16; Days needed=160÷16=10