Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 896 · 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. 1.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 1 day (c) 13 days (d) 22 days
2. 2.If 2 mangoes cost ₹34, how much do 7 mangoes cost? (a) ₹136 (b) ₹238 (c) ₹119 (d) ₹39
3. 3.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 13 days (c) 16 days (d) 12 days
4. 4.If 2 notebooks cost ₹8, how much do 7 notebooks cost? (a) ₹56 (b) ₹13 (c) ₹28 (d) ₹32
5. 5.If 2 kites cost ₹8, how much do 4 kites cost? (a) ₹32 (b) ₹10 (c) ₹16 (d) ₹20
6. 6.₹550 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹400 (b) ₹275 (c) ₹50 (d) ₹150
7. 7.If 2 notebooks cost ₹44, how much do 8 notebooks cost? (a) ₹50 (b) ₹352 (c) ₹176 (d) ₹198
8. 8.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 6 days (d) 20 days
9. 9.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹29 (b) ₹174 (c) ₹203 (d) ₹145
10. 10.If 3 pens cost ₹27, how much do 10 pens cost? (a) ₹90 (b) ₹270 (c) ₹99 (d) ₹34
11. 11.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 5 days (c) 6 days (d) 7 days
12. 12.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 28 days (d) 15 days
13. 13.If 9 notebooks cost ₹108, how much do 7 notebooks cost? (a) ₹106 (b) ₹96 (c) ₹84 (d) ₹756
14. 14.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 8 days
15. 15.₹84 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹42 (b) ₹84 (c) ₹28 (d) ₹56
16. 16.If 3 mangoes cost ₹54, how much do 7 mangoes cost? (a) ₹58 (b) ₹378 (c) ₹126 (d) ₹144
17. 17.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 15 days (c) 7 days (d) 34 days
18. 18.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹70 (b) ₹91 (c) ₹14 (d) ₹112
19. 19.If 9 kites cost ₹171, how much do 10 kites cost? (a) ₹1710 (b) ₹190 (c) ₹209 (d) ₹172
20. 20.If 9 mangoes cost ₹153, how much do 11 mangoes cost? (a) ₹204 (b) ₹155 (c) ₹1683 (d) ₹187
21. 21.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 9 days (d) 7 days
22. 22.If 6 kites cost ₹30, how much do 11 kites cost? (a) ₹35 (b) ₹330 (c) ₹60 (d) ₹55
23. 23.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹72 (b) ₹8 (c) ₹40 (d) ₹56
24. 24.If 4 notebooks cost ₹60, how much do 5 notebooks cost? (a) ₹300 (b) ₹90 (c) ₹61 (d) ₹75
25. 25.If 6 mangoes cost ₹60, how much do 12 mangoes cost? (a) ₹66 (b) ₹720 (c) ₹120 (d) ₹130
26. 26.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 21 days (d) 20 days
27. 27.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 16 days (d) 17 days
28. 28.₹93 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹62 (b) ₹93 (c) ₹31 (d) ₹63
29. 29.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 5 days (d) 16 days
30. 30.If 8 pens cost ₹192, how much do 2 pens cost? (a) ₹72 (b) ₹186 (c) ₹48 (d) ₹384
31. 31.If 3 kites cost ₹51, how much do 9 kites cost? (a) ₹459 (b) ₹170 (c) ₹153 (d) ₹57
32. 32.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 2 days (d) 7 days
33. 33.₹336 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹294 (b) ₹336 (c) ₹42 (d) ₹168
34. 34.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹44 (d) ₹48
35. 35.If 7 mangoes cost ₹49, how much do 8 mangoes cost? (a) ₹56 (b) ₹392 (c) ₹50 (d) ₹63
36. 36.If 6 pens cost ₹30, how much do 10 pens cost? (a) ₹50 (b) ₹55 (c) ₹300 (d) ₹34
37. 37.If 3 notebooks cost ₹24, how much do 12 notebooks cost? (a) ₹288 (b) ₹104 (c) ₹96 (d) ₹33
38. 38.If 4 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹96 (b) ₹46 (c) ₹24 (d) ₹36
39. 39.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹50 (b) ₹70 (c) ₹90 (d) ₹10
40. 40.If 7 mangoes cost ₹119, how much do 11 mangoes cost? (a) ₹1309 (b) ₹187 (c) ₹123 (d) ₹204

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