Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 130 · 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.₹175 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹50 (b) ₹125 (c) ₹150 (d) ₹25
2. 2.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 16 days (d) 5 days
3. 3.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹85 (b) ₹34 (c) ₹68 (d) ₹102
4. 4.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹21 (b) ₹189 (c) ₹84 (d) ₹210
5. 5.₹176 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹22 (b) ₹88 (c) ₹110 (d) ₹66
6. 6.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 9 days (d) 16 days
7. 7.If 5 mangoes cost ₹85, how much do 10 mangoes cost? (a) ₹850 (b) ₹90 (c) ₹170 (d) ₹187
8. 8.₹243 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹27 (b) ₹216 (c) ₹189 (d) ₹54
9. 9.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 2 days (d) 14 days
10. 10.If 2 notebooks cost ₹32, how much do 12 notebooks cost? (a) ₹42 (b) ₹384 (c) ₹208 (d) ₹192
11. 11.₹248 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹93 (b) ₹31 (c) ₹155 (d) ₹124
12. 12.If 8 notebooks cost ₹160, how much do 11 notebooks cost? (a) ₹163 (b) ₹1760 (c) ₹220 (d) ₹240
13. 13.If 2 kites cost ₹14, how much do 9 kites cost? (a) ₹63 (b) ₹126 (c) ₹70 (d) ₹21
14. 14.If 3 pens cost ₹12, how much do 5 pens cost? (a) ₹24 (b) ₹60 (c) ₹20 (d) ₹14
15. 15.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 6 days (d) 8 days
16. 16.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 7 days (d) 8 days
17. 17.₹160 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹144 (b) ₹80 (c) ₹16 (d) ₹160
18. 18.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 13 days (d) 27 days
19. 19.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹423 (b) ₹329 (c) ₹47 (d) ₹235
20. 20.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 4 days (d) 5 days
21. 21.₹225 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹200 (b) ₹50 (c) ₹25 (d) ₹175
22. 22.If 8 notebooks cost ₹192, how much do 3 notebooks cost? (a) ₹72 (b) ₹576 (c) ₹187 (d) ₹96
23. 23.If 8 notebooks cost ₹176, how much do 9 notebooks cost? (a) ₹220 (b) ₹177 (c) ₹1584 (d) ₹198
24. 24.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 4 days (d) 5 days
25. 25.If 2 pens cost ₹10, how much do 5 pens cost? (a) ₹25 (b) ₹30 (c) ₹13 (d) ₹50
26. 26.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹5 (b) ₹15 (c) ₹20 (d) ₹10
27. 27.₹104 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹91 (b) ₹52 (c) ₹13 (d) ₹104
28. 28.₹294 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹294 (b) ₹147 (c) ₹245 (d) ₹49
29. 29.If 6 kites cost ₹84, how much do 7 kites cost? (a) ₹98 (b) ₹112 (c) ₹588 (d) ₹85
30. 30.If 7 kites cost ₹42, how much do 8 kites cost? (a) ₹54 (b) ₹48 (c) ₹336 (d) ₹43
31. 31.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹162 (b) ₹27 (c) ₹135 (d) ₹189
32. 32.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 10 days (d) 7 days
33. 33.If 2 kites cost ₹50, how much do 9 kites cost? (a) ₹450 (b) ₹250 (c) ₹57 (d) ₹225
34. 34.If 4 notebooks cost ₹16, how much do 9 notebooks cost? (a) ₹40 (b) ₹21 (c) ₹144 (d) ₹36
35. 35.If 8 pens cost ₹112, how much do 12 pens cost? (a) ₹116 (b) ₹1344 (c) ₹168 (d) ₹182
36. 36.If 4 mangoes cost ₹88, how much do 5 mangoes cost? (a) ₹89 (b) ₹110 (c) ₹132 (d) ₹440
37. 37.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 4 days (d) 11 days
38. 38.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 15 days (c) 2 days (d) 14 days
39. 39.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹39 (b) ₹234 (c) ₹195 (d) ₹156
40. 40.If 7 pens cost ₹133, how much do 11 pens cost? (a) ₹1463 (b) ₹137 (c) ₹228 (d) ₹209

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