Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 90 · 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 2 pens cost ₹46, how much do 6 pens cost? (a) ₹50 (b) ₹276 (c) ₹138 (d) ₹161
2. 2.If 4 kites cost ₹48, how much do 6 kites cost? (a) ₹288 (b) ₹72 (c) ₹84 (d) ₹50
3. 3.If 9 pens cost ₹225, how much do 11 pens cost? (a) ₹2475 (b) ₹300 (c) ₹227 (d) ₹275
4. 4.If 7 notebooks cost ₹154, how much do 8 notebooks cost? (a) ₹1232 (b) ₹198 (c) ₹176 (d) ₹155
5. 5.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 9 days (c) 13 days (d) 23 days
6. 6.₹240 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹96 (b) ₹48 (c) ₹144 (d) ₹120
7. 7.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹135 (b) ₹108 (c) ₹27 (d) ₹162
8. 8.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 17 days (d) 10 days
9. 9.If 3 mangoes cost ₹72, how much do 6 mangoes cost? (a) ₹144 (b) ₹75 (c) ₹168 (d) ₹432
10. 10.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 45 days (d) 5 days
11. 11.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 11 days (d) 2 days
12. 12.If 4 pens cost ₹80, how much do 10 pens cost? (a) ₹800 (b) ₹200 (c) ₹220 (d) ₹86
13. 13.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 4 days (d) 2 days
14. 14.₹115 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹46 (d) ₹69
15. 15.If 2 mangoes cost ₹6, how much do 7 mangoes cost? (a) ₹24 (b) ₹42 (c) ₹11 (d) ₹21
16. 16.If 8 pens cost ₹112, how much do 5 pens cost? (a) ₹109 (b) ₹70 (c) ₹84 (d) ₹560
17. 17.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 4 days (d) 2 days
18. 18.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹112 (b) ₹16 (c) ₹32 (d) ₹72
19. 19.₹195 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹156 (b) ₹39 (c) ₹78 (d) ₹117
20. 20.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
21. 21.If 2 mangoes cost ₹24, how much do 7 mangoes cost? (a) ₹96 (b) ₹168 (c) ₹84 (d) ₹29
22. 22.If 8 notebooks cost ₹104, how much do 6 notebooks cost? (a) ₹91 (b) ₹102 (c) ₹78 (d) ₹624
23. 23.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 6 days
24. 24.₹196 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹14 (b) ₹98 (c) ₹70 (d) ₹126
25. 25.₹162 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹18 (c) ₹81 (d) ₹162
26. 26.₹210 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹180 (b) ₹105 (c) ₹210 (d) ₹30
27. 27.If 9 notebooks cost ₹90, how much do 8 notebooks cost? (a) ₹89 (b) ₹80 (c) ₹90 (d) ₹720
28. 28.₹253 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹92 (b) ₹161 (c) ₹184 (d) ₹23
29. 29.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹35 (b) ₹40 (c) ₹30 (d) ₹10
30. 30.If 6 notebooks cost ₹102, how much do 2 notebooks cost? (a) ₹98 (b) ₹34 (c) ₹51 (d) ₹204
31. 31.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 9 days (d) 5 days
32. 32.If 3 notebooks cost ₹72, how much do 8 notebooks cost? (a) ₹216 (b) ₹576 (c) ₹192 (d) ₹77
33. 33.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 6 days (d) 48 days
34. 34.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹46 (b) ₹299 (c) ₹184 (d) ₹414
35. 35.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹41 (b) ₹369 (c) ₹205 (d) ₹328
36. 36.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹18 (b) ₹24 (c) ₹30 (d) ₹6
37. 37.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 4 days (d) 9 days
38. 38.₹205 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹165 (b) ₹41 (c) ₹164 (d) ₹205
39. 39.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 8 days (d) 7 days
40. 40.If 7 notebooks cost ₹91, how much do 2 notebooks cost? (a) ₹182 (b) ₹86 (c) ₹26 (d) ₹39

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