Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 533 · 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) ₹12 (b) ₹15 (c) ₹18 (d) ₹84
2. 2.If 3 kites cost ₹75, how much do 6 kites cost? (a) ₹78 (b) ₹450 (c) ₹150 (d) ₹175
3. 3.If 5 mangoes cost ₹115, how much do 10 mangoes cost? (a) ₹120 (b) ₹1150 (c) ₹253 (d) ₹230
4. 4.₹231 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹147 (b) ₹168 (c) ₹84 (d) ₹21
5. 5.If 9 mangoes cost ₹117, how much do 10 mangoes cost? (a) ₹143 (b) ₹130 (c) ₹1170 (d) ₹118
6. 6.If 6 mangoes cost ₹132, how much do 8 mangoes cost? (a) ₹198 (b) ₹1056 (c) ₹176 (d) ₹134
7. 7.If 8 kites cost ₹136, how much do 3 kites cost? (a) ₹51 (b) ₹131 (c) ₹408 (d) ₹68
8. 8.If 3 mangoes cost ₹33, how much do 8 mangoes cost? (a) ₹88 (b) ₹99 (c) ₹38 (d) ₹264
9. 9.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 16 days (d) 9 days
10. 10.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 19 days (d) 20 days
11. 11.If 4 kites cost ₹84, how much do 9 kites cost? (a) ₹210 (b) ₹89 (c) ₹756 (d) ₹189
12. 12.₹217 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹62 (b) ₹31 (c) ₹186 (d) ₹155
13. 13.If 3 pens cost ₹63, how much do 10 pens cost? (a) ₹630 (b) ₹210 (c) ₹70 (d) ₹231
14. 14.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹238 (b) ₹34 (c) ₹187 (d) ₹136
15. 15.₹90 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹81 (b) ₹9 (c) ₹90 (d) ₹45
16. 16.If 7 pens cost ₹49, how much do 2 pens cost? (a) ₹44 (b) ₹21 (c) ₹98 (d) ₹14
17. 17.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 15 days (d) 3 days
18. 18.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹450 (b) ₹250 (c) ₹350 (d) ₹50
19. 19.If 2 notebooks cost ₹38, how much do 12 notebooks cost? (a) ₹48 (b) ₹228 (c) ₹456 (d) ₹247
20. 20.If 2 mangoes cost ₹50, how much do 6 mangoes cost? (a) ₹150 (b) ₹175 (c) ₹54 (d) ₹300
21. 21.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 9 days (d) 7 days
22. 22.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹91 (b) ₹78 (c) ₹65 (d) ₹13
23. 23.If 7 mangoes cost ₹133, how much do 8 mangoes cost? (a) ₹152 (b) ₹1064 (c) ₹171 (d) ₹134
24. 24.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 11 days (d) 12 days
25. 25.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹21 (b) ₹126 (c) ₹147 (d) ₹105
26. 26.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹52 (b) ₹39 (c) ₹26 (d) ₹78
27. 27.If 2 kites cost ₹32, how much do 10 kites cost? (a) ₹40 (b) ₹160 (c) ₹176 (d) ₹320
28. 28.If 7 kites cost ₹98, how much do 9 kites cost? (a) ₹882 (b) ₹126 (c) ₹100 (d) ₹140
29. 29.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹78 (b) ₹13 (c) ₹65 (d) ₹52
30. 30.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 9 days (d) 15 days
31. 31.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹50 (b) ₹25 (c) ₹45 (d) ₹5
32. 32.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
33. 33.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 8 days (d) 10 days
34. 34.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 26 days (d) 11 days
35. 35.If 3 kites cost ₹24, how much do 8 kites cost? (a) ₹72 (b) ₹64 (c) ₹192 (d) ₹29
36. 36.If 6 kites cost ₹132, how much do 9 kites cost? (a) ₹198 (b) ₹220 (c) ₹1188 (d) ₹135
37. 37.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 8 days (d) 20 days
38. 38.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹57 (b) ₹19 (c) ₹39 (d) ₹38
39. 39.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 10 days (c) 20 days (d) 14 days
40. 40.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 2 days (d) 4 days

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