Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 749 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.₹169 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹52 (b) ₹130 (c) ₹117 (d) ₹13
2. 2.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 9 days (d) 8 days
3. 3.If 6 kites cost ₹126, how much do 4 kites cost? (a) ₹504 (b) ₹105 (c) ₹84 (d) ₹124
4. 4.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 11 days (d) 2 days
5. 5.₹72 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹60 (b) ₹36 (c) ₹72 (d) ₹12
6. 6.₹117 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹104 (b) ₹105 (c) ₹117 (d) ₹13
7. 7.If 9 pens cost ₹180, how much do 10 pens cost? (a) ₹220 (b) ₹1800 (c) ₹181 (d) ₹200
8. 8.₹360 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹280 (b) ₹180 (c) ₹40 (d) ₹80
9. 9.If 9 mangoes cost ₹225, how much do 10 mangoes cost? (a) ₹226 (b) ₹2250 (c) ₹250 (d) ₹275
10. 10.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 19 days (c) 21 days (d) 11 days
11. 11.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 8 days (d) 6 days
12. 12.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 32 days (c) 33 days (d) 17 days
13. 13.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 10 days (d) 18 days
14. 14.If 7 mangoes cost ₹42, how much do 11 mangoes cost? (a) ₹46 (b) ₹66 (c) ₹72 (d) ₹462
15. 15.₹286 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹22 (b) ₹143 (c) ₹88 (d) ₹198
16. 16.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 28 days (d) 18 days
17. 17.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 5 days (d) 15 days
18. 18.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 2 days (d) 9 days
19. 19.If 9 kites cost ₹171, how much do 5 kites cost? (a) ₹95 (b) ₹114 (c) ₹855 (d) ₹167
20. 20.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 7 days (d) 16 days
21. 21.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 33 days (c) 17 days (d) 34 days
22. 22.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 20 days (d) 36 days
23. 23.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 18 days (c) 17 days (d) 19 days
24. 24.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 17 days (d) 13 days
25. 25.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹432 (b) ₹312 (c) ₹192 (d) ₹48
26. 26.If 2 mangoes cost ₹22, how much do 5 mangoes cost? (a) ₹55 (b) ₹25 (c) ₹110 (d) ₹66
27. 27.₹110 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹77 (b) ₹33 (c) ₹11 (d) ₹55
28. 28.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 9 days (d) 6 days
29. 29.If 8 mangoes cost ₹152, how much do 7 mangoes cost? (a) ₹1064 (b) ₹133 (c) ₹152 (d) ₹151
30. 30.If 8 kites cost ₹200, how much do 4 kites cost? (a) ₹196 (b) ₹125 (c) ₹800 (d) ₹100
31. 31.₹209 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹171 (b) ₹57 (c) ₹19 (d) ₹152
32. 32.₹143 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹13 (b) ₹117 (c) ₹26 (d) ₹130
33. 33.If 6 notebooks cost ₹66, how much do 7 notebooks cost? (a) ₹77 (b) ₹67 (c) ₹462 (d) ₹88
34. 34.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 7 days
35. 35.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 2 days (d) 8 days
36. 36.If 5 mangoes cost ₹120, how much do 8 mangoes cost? (a) ₹123 (b) ₹960 (c) ₹216 (d) ₹192
37. 37.If 8 mangoes cost ₹152, how much do 9 mangoes cost? (a) ₹171 (b) ₹1368 (c) ₹153 (d) ₹190
38. 38.If 7 notebooks cost ₹77, how much do 5 notebooks cost? (a) ₹385 (b) ₹66 (c) ₹75 (d) ₹55
39. 39.If 3 notebooks cost ₹18, how much do 9 notebooks cost? (a) ₹60 (b) ₹24 (c) ₹54 (d) ₹162
40. 40.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹64 (b) ₹80 (c) ₹16 (d) ₹72

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