Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 73 · 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 ₹160, how much do 3 notebooks cost? (a) ₹80 (b) ₹60 (c) ₹155 (d) ₹480
2. 2.If 5 kites cost ₹95, how much do 6 kites cost? (a) ₹133 (b) ₹96 (c) ₹114 (d) ₹570
3. 3.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹20 (b) ₹5 (c) ₹30 (d) ₹25
4. 4.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 20 days (d) 15 days
5. 5.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹11 (b) ₹99 (c) ₹55 (d) ₹77
6. 6.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹25 (b) ₹100 (c) ₹250 (d) ₹225
7. 7.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 7 days (d) 11 days
8. 8.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹414 (b) ₹46 (c) ₹184 (d) ₹299
9. 9.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 3 days (d) 6 days
10. 10.If 8 pens cost ₹168, how much do 9 pens cost? (a) ₹1512 (b) ₹189 (c) ₹169 (d) ₹210
11. 11.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹12 (b) ₹18 (c) ₹15 (d) ₹6
12. 12.₹250 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹125 (b) ₹50 (c) ₹250 (d) ₹200
13. 13.If 7 notebooks cost ₹161, how much do 12 notebooks cost? (a) ₹299 (b) ₹276 (c) ₹1932 (d) ₹166
14. 14.₹416 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹32 (b) ₹128 (c) ₹288 (d) ₹208
15. 15.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 36 days (c) 4 days (d) 16 days
16. 16.If 2 pens cost ₹44, how much do 3 pens cost? (a) ₹88 (b) ₹66 (c) ₹45 (d) ₹132
17. 17.If 2 notebooks cost ₹38, how much do 6 notebooks cost? (a) ₹42 (b) ₹114 (c) ₹133 (d) ₹228
18. 18.If 6 notebooks cost ₹60, how much do 5 notebooks cost? (a) ₹300 (b) ₹60 (c) ₹50 (d) ₹59
19. 19.If 6 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹60 (b) ₹40 (c) ₹360 (d) ₹66
20. 20.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹230 (b) ₹46 (c) ₹253 (d) ₹276
21. 21.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 15 days (d) 13 days
22. 22.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 35 days (c) 5 days (d) 36 days
23. 23.If 7 mangoes cost ₹49, how much do 6 mangoes cost? (a) ₹294 (b) ₹48 (c) ₹49 (d) ₹42
24. 24.If 5 mangoes cost ₹25, how much do 12 mangoes cost? (a) ₹32 (b) ₹300 (c) ₹60 (d) ₹65
25. 25.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 19 days (d) 4 days
26. 26.If 5 mangoes cost ₹85, how much do 6 mangoes cost? (a) ₹86 (b) ₹119 (c) ₹102 (d) ₹510
27. 27.₹143 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹88 (b) ₹11 (c) ₹99 (d) ₹55
28. 28.₹333 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹37 (b) ₹222 (c) ₹185 (d) ₹148
29. 29.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹74 (b) ₹370 (c) ₹37 (d) ₹333
30. 30.₹252 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹126 (b) ₹28 (c) ₹252 (d) ₹224
31. 31.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 13 days (d) 15 days
32. 32.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 5 days (d) 4 days
33. 33.If 7 mangoes cost ₹175, how much do 9 mangoes cost? (a) ₹177 (b) ₹225 (c) ₹1575 (d) ₹250
34. 34.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 15 days (d) 3 days
35. 35.If 4 pens cost ₹20, how much do 8 pens cost? (a) ₹160 (b) ₹24 (c) ₹45 (d) ₹40
36. 36.If 9 mangoes cost ₹198, how much do 10 mangoes cost? (a) ₹220 (b) ₹242 (c) ₹199 (d) ₹1980
37. 37.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 2 days (c) 14 days (d) 32 days
38. 38.If 4 mangoes cost ₹72, how much do 2 mangoes cost? (a) ₹36 (b) ₹144 (c) ₹54 (d) ₹70
39. 39.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 7 days (c) 52 days (d) 19 days
40. 40.If 2 kites cost ₹20, how much do 10 kites cost? (a) ₹28 (b) ₹200 (c) ₹100 (d) ₹110

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