Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 232 · 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.If 7 notebooks cost ₹21, how much do 4 notebooks cost? (a) ₹84 (b) ₹15 (c) ₹18 (d) ₹12
2. 2.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 39 days (c) 40 days (d) 19 days
3. 3.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 8 days (d) 7 days
4. 4.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 13 days (d) 17 days
5. 5.₹155 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹31 (b) ₹93 (c) ₹124 (d) ₹62
6. 6.If 9 pens cost ₹36, how much do 6 pens cost? (a) ₹33 (b) ₹24 (c) ₹216 (d) ₹28
7. 7.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 53 days (d) 52 days
8. 8.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 13 days (d) 17 days
9. 9.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 7 days (d) 25 days
10. 10.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹99 (b) ₹144 (c) ₹18 (d) ₹54
11. 11.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 1 day
12. 12.If 5 kites cost ₹125, how much do 6 kites cost? (a) ₹150 (b) ₹750 (c) ₹175 (d) ₹126
13. 13.If 2 mangoes cost ₹34, how much do 11 mangoes cost? (a) ₹187 (b) ₹43 (c) ₹374 (d) ₹204
14. 14.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹17 (b) ₹170 (c) ₹68 (d) ₹153
15. 15.If 6 notebooks cost ₹30, how much do 4 notebooks cost? (a) ₹25 (b) ₹28 (c) ₹20 (d) ₹120
16. 16.₹495 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹360 (b) ₹315 (c) ₹180 (d) ₹45
17. 17.₹152 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹76 (b) ₹152 (c) ₹19 (d) ₹133
18. 18.₹110 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹11 (b) ₹33 (c) ₹55 (d) ₹77
19. 19.If 5 mangoes cost ₹40, how much do 6 mangoes cost? (a) ₹48 (b) ₹56 (c) ₹240 (d) ₹41
20. 20.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 9 days (d) 16 days
21. 21.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 13 days (c) 9 days (d) 22 days
22. 22.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹24 (b) ₹36 (c) ₹30 (d) ₹12
23. 23.If 9 kites cost ₹171, how much do 10 kites cost? (a) ₹1710 (b) ₹209 (c) ₹190 (d) ₹172
24. 24.If 3 mangoes cost ₹54, how much do 9 mangoes cost? (a) ₹60 (b) ₹162 (c) ₹180 (d) ₹486
25. 25.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 24 days (b) 6 days (c) 7 days (d) 18 days
26. 26.If 3 pens cost ₹18, how much do 11 pens cost? (a) ₹72 (b) ₹26 (c) ₹66 (d) ₹198
27. 27.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 42 days (c) 18 days (d) 10 days
28. 28.₹80 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹80 (d) ₹72
29. 29.₹200 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹100 (b) ₹40 (c) ₹200 (d) ₹160
30. 30.If 3 mangoes cost ₹15, how much do 6 mangoes cost? (a) ₹18 (b) ₹90 (c) ₹30 (d) ₹35
31. 31.If 5 notebooks cost ₹95, how much do 12 notebooks cost? (a) ₹102 (b) ₹247 (c) ₹1140 (d) ₹228
32. 32.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 24 days (c) 17 days (d) 6 days
33. 33.If 8 notebooks cost ₹56, how much do 9 notebooks cost? (a) ₹70 (b) ₹504 (c) ₹57 (d) ₹63
34. 34.₹405 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹405 (b) ₹360 (c) ₹361 (d) ₹45
35. 35.If 4 pens cost ₹24, how much do 8 pens cost? (a) ₹54 (b) ₹192 (c) ₹28 (d) ₹48
36. 36.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 5 days (c) 34 days (d) 17 days
37. 37.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 1 day (d) 21 days
38. 38.₹340 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹170 (b) ₹306 (c) ₹340 (d) ₹34
39. 39.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹102 (b) ₹85 (c) ₹68 (d) ₹34
40. 40.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 24 days (c) 16 days (d) 8 days

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