Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 610 · 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.₹100 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹100 (b) ₹80 (c) ₹50 (d) ₹20
2. 2.If 5 kites cost ₹100, how much do 4 kites cost? (a) ₹100 (b) ₹400 (c) ₹80 (d) ₹99
3. 3.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 9 days
4. 4.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹40 (b) ₹45 (c) ₹5 (d) ₹25
5. 5.If 5 pens cost ₹40, how much do 8 pens cost? (a) ₹43 (b) ₹64 (c) ₹72 (d) ₹320
6. 6.₹352 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹160 (b) ₹176 (c) ₹32 (d) ₹192
7. 7.If 4 mangoes cost ₹56, how much do 2 mangoes cost? (a) ₹42 (b) ₹112 (c) ₹54 (d) ₹28
8. 8.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 17 days
9. 9.If 6 mangoes cost ₹30, how much do 4 mangoes cost? (a) ₹25 (b) ₹20 (c) ₹28 (d) ₹120
10. 10.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹225 (b) ₹250 (c) ₹100 (d) ₹25
11. 11.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 2 days
12. 12.If 8 pens cost ₹184, how much do 5 pens cost? (a) ₹181 (b) ₹920 (c) ₹115 (d) ₹138
13. 13.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹81 (b) ₹45 (c) ₹63 (d) ₹9
14. 14.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 21 days (d) 5 days
15. 15.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 17 days (d) 11 days
16. 16.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹15 (b) ₹61 (c) ₹75 (d) ₹60
17. 17.If 8 pens cost ₹128, how much do 6 pens cost? (a) ₹768 (b) ₹126 (c) ₹112 (d) ₹96
18. 18.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 4 days (d) 2 days
19. 19.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 10 days (d) 8 days
20. 20.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹322 (b) ₹46 (c) ₹276 (d) ₹230
21. 21.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 2 days (d) 4 days
22. 22.If 7 notebooks cost ₹112, how much do 8 notebooks cost? (a) ₹113 (b) ₹896 (c) ₹128 (d) ₹144
23. 23.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 9 days (d) 8 days
24. 24.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹26 (b) ₹169 (c) ₹208 (d) ₹130
25. 25.If 6 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹27 (b) ₹108 (c) ₹18 (d) ₹50
26. 26.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 7 days (c) 19 days (d) 40 days
27. 27.If 3 mangoes cost ₹18, how much do 5 mangoes cost? (a) ₹30 (b) ₹20 (c) ₹90 (d) ₹36
28. 28.₹99 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹45 (b) ₹54 (c) ₹63 (d) ₹9
29. 29.If 2 mangoes cost ₹6, how much do 4 mangoes cost? (a) ₹12 (b) ₹8 (c) ₹15 (d) ₹24
30. 30.If 4 kites cost ₹88, how much do 8 kites cost? (a) ₹176 (b) ₹198 (c) ₹92 (d) ₹704
31. 31.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 9 days (d) 13 days
32. 32.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 3 days (d) 4 days
33. 33.If 3 notebooks cost ₹24, how much do 2 notebooks cost? (a) ₹23 (b) ₹48 (c) ₹24 (d) ₹16
34. 34.If 4 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹36 (b) ₹120 (c) ₹30 (d) ₹25
35. 35.If 6 pens cost ₹138, how much do 3 pens cost? (a) ₹135 (b) ₹69 (c) ₹92 (d) ₹414
36. 36.If 5 mangoes cost ₹85, how much do 6 mangoes cost? (a) ₹510 (b) ₹119 (c) ₹86 (d) ₹102
37. 37.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 5 days
38. 38.If 6 notebooks cost ₹30, how much do 3 notebooks cost? (a) ₹90 (b) ₹15 (c) ₹20 (d) ₹27
39. 39.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 1 day (d) 2 days
40. 40.If 7 notebooks cost ₹28, how much do 8 notebooks cost? (a) ₹36 (b) ₹32 (c) ₹224 (d) ₹29

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