Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 313 · 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.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹21 (b) ₹147 (c) ₹126 (d) ₹105
2. 2.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 5 days (d) 22 days
3. 3.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 3 days (d) 6 days
4. 4.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 22 days (c) 21 days (d) 9 days
5. 5.If 5 mangoes cost ₹45, how much do 6 mangoes cost? (a) ₹63 (b) ₹54 (c) ₹46 (d) ₹270
6. 6.₹196 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹196 (b) ₹28 (c) ₹98 (d) ₹168
7. 7.If 6 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹108 (b) ₹18 (c) ₹27 (d) ₹50
8. 8.₹392 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹196 (b) ₹49 (c) ₹392 (d) ₹343
9. 9.If 9 kites cost ₹99, how much do 4 kites cost? (a) ₹396 (b) ₹94 (c) ₹55 (d) ₹44
10. 10.If 7 notebooks cost ₹28, how much do 9 notebooks cost? (a) ₹30 (b) ₹40 (c) ₹252 (d) ₹36
11. 11.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 7 days (d) 6 days
12. 12.If 2 mangoes cost ₹16, how much do 5 mangoes cost? (a) ₹40 (b) ₹80 (c) ₹48 (d) ₹19
13. 13.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 2 days (c) 10 days (d) 14 days
14. 14.₹308 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹28 (b) ₹154 (c) ₹224 (d) ₹84
15. 15.₹352 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹176 (b) ₹32 (c) ₹128 (d) ₹224
16. 16.If 4 kites cost ₹60, how much do 2 kites cost? (a) ₹120 (b) ₹45 (c) ₹30 (d) ₹58
17. 17.If 2 kites cost ₹40, how much do 10 kites cost? (a) ₹48 (b) ₹200 (c) ₹400 (d) ₹220
18. 18.If 3 pens cost ₹60, how much do 2 pens cost? (a) ₹120 (b) ₹59 (c) ₹40 (d) ₹60
19. 19.₹78 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹39 (b) ₹78 (c) ₹65 (d) ₹13
20. 20.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 11 days
21. 21.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹160 (b) ₹32 (c) ₹192 (d) ₹224
22. 22.If 8 kites cost ₹88, how much do 10 kites cost? (a) ₹880 (b) ₹90 (c) ₹110 (d) ₹121
23. 23.If 9 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹44 (b) ₹360 (c) ₹40 (d) ₹37
24. 24.If 5 notebooks cost ₹65, how much do 8 notebooks cost? (a) ₹117 (b) ₹520 (c) ₹104 (d) ₹68
25. 25.If 5 kites cost ₹125, how much do 4 kites cost? (a) ₹124 (b) ₹500 (c) ₹100 (d) ₹125
26. 26.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 24 days (c) 25 days (d) 18 days
27. 27.₹164 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹41 (b) ₹123 (c) ₹82 (d) ₹164
28. 28.If 5 notebooks cost ₹70, how much do 2 notebooks cost? (a) ₹67 (b) ₹140 (c) ₹28 (d) ₹42
29. 29.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 10 days (d) 1 day
30. 30.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 8 days (d) 11 days
31. 31.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 20 days (c) 11 days (d) 21 days
32. 32.₹54 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹27 (b) ₹6 (c) ₹48 (d) ₹54
33. 33.If 4 mangoes cost ₹36, how much do 12 mangoes cost? (a) ₹117 (b) ₹432 (c) ₹108 (d) ₹44
34. 34.₹180 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹80 (b) ₹20 (c) ₹100 (d) ₹90
35. 35.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 3 days (d) 27 days
36. 36.If 7 mangoes cost ₹21, how much do 10 mangoes cost? (a) ₹210 (b) ₹33 (c) ₹24 (d) ₹30
37. 37.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹31 (b) ₹279 (c) ₹217 (d) ₹155
38. 38.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 5 days (d) 3 days
39. 39.If 7 notebooks cost ₹168, how much do 12 notebooks cost? (a) ₹288 (b) ₹173 (c) ₹312 (d) ₹2016
40. 40.If 6 notebooks cost ₹48, how much do 8 notebooks cost? (a) ₹384 (b) ₹64 (c) ₹50 (d) ₹72

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