Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 971 · 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 4 mangoes cost ₹16, how much do 8 mangoes cost? (a) ₹32 (b) ₹128 (c) ₹36 (d) ₹20
2. 2.₹40 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹20 (b) ₹5 (c) ₹35 (d) ₹40
3. 3.₹192 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹96 (d) ₹192
4. 4.If 5 notebooks cost ₹35, how much do 3 notebooks cost? (a) ₹28 (b) ₹21 (c) ₹105 (d) ₹33
5. 5.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 8 days (d) 3 days
6. 6.If 9 notebooks cost ₹225, how much do 8 notebooks cost? (a) ₹224 (b) ₹225 (c) ₹200 (d) ₹1800
7. 7.If 6 mangoes cost ₹30, how much do 9 mangoes cost? (a) ₹45 (b) ₹270 (c) ₹33 (d) ₹50
8. 8.₹200 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹50 (b) ₹150 (c) ₹200 (d) ₹100
9. 9.If 7 notebooks cost ₹119, how much do 6 notebooks cost? (a) ₹714 (b) ₹119 (c) ₹118 (d) ₹102
10. 10.₹310 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹93 (b) ₹217 (c) ₹31 (d) ₹155
11. 11.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹16 (c) ₹48 (d) ₹32
12. 12.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 9 days (d) 21 days
13. 13.If 5 kites cost ₹25, how much do 12 kites cost? (a) ₹32 (b) ₹60 (c) ₹300 (d) ₹65
14. 14.If 3 mangoes cost ₹24, how much do 7 mangoes cost? (a) ₹64 (b) ₹168 (c) ₹28 (d) ₹56
15. 15.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 4 days (d) 5 days
16. 16.₹70 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹70 (b) ₹35 (c) ₹14 (d) ₹56
17. 17.₹85 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹69 (b) ₹17 (c) ₹85 (d) ₹68
18. 18.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 16 days (d) 11 days
19. 19.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹208 (b) ₹26 (c) ₹169 (d) ₹130
20. 20.If 2 mangoes cost ₹22, how much do 7 mangoes cost? (a) ₹154 (b) ₹77 (c) ₹88 (d) ₹27
21. 21.₹48 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹48 (b) ₹42 (c) ₹6 (d) ₹24
22. 22.If 7 pens cost ₹105, how much do 5 pens cost? (a) ₹90 (b) ₹103 (c) ₹75 (d) ₹525
23. 23.₹117 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹39 (b) ₹117 (c) ₹79 (d) ₹78
24. 24.If 5 mangoes cost ₹55, how much do 2 mangoes cost? (a) ₹33 (b) ₹52 (c) ₹22 (d) ₹110
25. 25.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 6 days (d) 7 days
26. 26.If 6 notebooks cost ₹120, how much do 3 notebooks cost? (a) ₹60 (b) ₹80 (c) ₹117 (d) ₹360
27. 27.If 3 kites cost ₹63, how much do 9 kites cost? (a) ₹69 (b) ₹567 (c) ₹210 (d) ₹189
28. 28.If 7 pens cost ₹126, how much do 9 pens cost? (a) ₹180 (b) ₹162 (c) ₹1134 (d) ₹128
29. 29.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 5 days (d) 6 days
30. 30.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹161 (b) ₹115 (c) ₹207 (d) ₹23
31. 31.If 2 kites cost ₹32, how much do 6 kites cost? (a) ₹112 (b) ₹96 (c) ₹36 (d) ₹192
32. 32.If 8 notebooks cost ₹32, how much do 2 notebooks cost? (a) ₹26 (b) ₹64 (c) ₹12 (d) ₹8
33. 33.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 4 days (c) 16 days (d) 41 days
34. 34.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 15 days (c) 8 days (d) 14 days
35. 35.If 5 pens cost ₹115, how much do 12 pens cost? (a) ₹1380 (b) ₹299 (c) ₹122 (d) ₹276
36. 36.If 5 pens cost ₹110, how much do 6 pens cost? (a) ₹111 (b) ₹154 (c) ₹660 (d) ₹132
37. 37.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹27 (b) ₹189 (c) ₹81 (d) ₹135
38. 38.₹119 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹102 (b) ₹34 (c) ₹17 (d) ₹85
39. 39.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹153 (b) ₹34 (c) ₹136 (d) ₹170
40. 40.₹294 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹42 (b) ₹147 (c) ₹252 (d) ₹294

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