Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 797 · 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 8 notebooks cost ₹176, how much do 11 notebooks cost? (a) ₹264 (b) ₹179 (c) ₹242 (d) ₹1936
2. 2.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹144 (b) ₹64 (c) ₹104 (d) ₹16
3. 3.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 43 days (c) 10 days (d) 42 days
4. 4.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 7 days (d) 6 days
5. 5.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 1 day
6. 6.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹10 (b) ₹35 (c) ₹50 (d) ₹20
7. 7.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹189 (b) ₹243 (c) ₹27 (d) ₹135
8. 8.₹175 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹150 (b) ₹25 (c) ₹151 (d) ₹175
9. 9.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 20 days (c) 56 days (d) 57 days
10. 10.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 15 days (d) 13 days
11. 11.If 2 pens cost ₹42, how much do 5 pens cost? (a) ₹126 (b) ₹210 (c) ₹105 (d) ₹45
12. 12.If 8 pens cost ₹32, how much do 7 pens cost? (a) ₹32 (b) ₹224 (c) ₹28 (d) ₹31
13. 13.If 7 pens cost ₹126, how much do 3 pens cost? (a) ₹72 (b) ₹122 (c) ₹54 (d) ₹378
14. 14.₹234 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹234 (b) ₹39 (c) ₹117 (d) ₹195
15. 15.If 4 kites cost ₹100, how much do 5 kites cost? (a) ₹101 (b) ₹150 (c) ₹125 (d) ₹500
16. 16.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 6 days
17. 17.If 4 mangoes cost ₹92, how much do 6 mangoes cost? (a) ₹552 (b) ₹94 (c) ₹138 (d) ₹161
18. 18.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 4 days (d) 2 days
19. 19.₹420 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹210 (b) ₹126 (c) ₹42 (d) ₹294
20. 20.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 11 days (c) 36 days (d) 17 days
21. 21.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹45 (c) ₹80 (d) ₹10
22. 22.₹539 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹98 (b) ₹49 (c) ₹490 (d) ₹441
23. 23.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 2 days (d) 4 days
24. 24.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 45 days (d) 23 days
25. 25.If 6 notebooks cost ₹18, how much do 11 notebooks cost? (a) ₹198 (b) ₹23 (c) ₹36 (d) ₹33
26. 26.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 2 days (d) 1 day
27. 27.₹70 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹70 (d) ₹63
28. 28.If 3 pens cost ₹12, how much do 4 pens cost? (a) ₹20 (b) ₹48 (c) ₹16 (d) ₹13
29. 29.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹216 (b) ₹243 (c) ₹27 (d) ₹135
30. 30.₹574 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹205 (b) ₹369 (c) ₹287 (d) ₹41
31. 31.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹32 (c) ₹96 (d) ₹64
32. 32.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹95 (b) ₹19 (c) ₹114 (d) ₹133
33. 33.If 6 pens cost ₹144, how much do 4 pens cost? (a) ₹120 (b) ₹576 (c) ₹96 (d) ₹142
34. 34.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 19 days (c) 18 days (d) 12 days
35. 35.If 6 notebooks cost ₹132, how much do 9 notebooks cost? (a) ₹220 (b) ₹135 (c) ₹1188 (d) ₹198
36. 36.If 2 pens cost ₹22, how much do 5 pens cost? (a) ₹110 (b) ₹25 (c) ₹55 (d) ₹66
37. 37.If 7 pens cost ₹147, how much do 11 pens cost? (a) ₹151 (b) ₹231 (c) ₹252 (d) ₹1617
38. 38.₹319 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹232 (b) ₹203 (c) ₹116 (d) ₹29
39. 39.If 7 kites cost ₹147, how much do 4 kites cost? (a) ₹105 (b) ₹588 (c) ₹144 (d) ₹84
40. 40.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 5 days (d) 20 days

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