Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 48 · 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 3 pens cost ₹42, how much do 4 pens cost? (a) ₹70 (b) ₹56 (c) ₹168 (d) ₹43
2. 2.If 6 notebooks cost ₹90, how much do 3 notebooks cost? (a) ₹45 (b) ₹87 (c) ₹60 (d) ₹270
3. 3.If 7 pens cost ₹21, how much do 4 pens cost? (a) ₹15 (b) ₹18 (c) ₹12 (d) ₹84
4. 4.₹182 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹130 (b) ₹26 (c) ₹52 (d) ₹91
5. 5.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 17 days (c) 5 days (d) 44 days
6. 6.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 15 days (d) 5 days
7. 7.₹234 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹90 (b) ₹117 (c) ₹144 (d) ₹18
8. 8.If 5 mangoes cost ₹90, how much do 7 mangoes cost? (a) ₹630 (b) ₹92 (c) ₹144 (d) ₹126
9. 9.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 53 days (c) 19 days (d) 52 days
10. 10.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 26 days (d) 27 days
11. 11.If 2 pens cost ₹22, how much do 5 pens cost? (a) ₹55 (b) ₹25 (c) ₹110 (d) ₹66
12. 12.If 7 pens cost ₹49, how much do 9 pens cost? (a) ₹70 (b) ₹51 (c) ₹441 (d) ₹63
13. 13.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹30 (d) ₹10
14. 14.If 7 notebooks cost ₹21, how much do 12 notebooks cost? (a) ₹39 (b) ₹36 (c) ₹26 (d) ₹252
15. 15.If 2 pens cost ₹8, how much do 7 pens cost? (a) ₹28 (b) ₹32 (c) ₹56 (d) ₹13
16. 16.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 16 days (d) 10 days
17. 17.If 6 kites cost ₹72, how much do 8 kites cost? (a) ₹108 (b) ₹96 (c) ₹576 (d) ₹74
18. 18.If 2 mangoes cost ₹6, how much do 12 mangoes cost? (a) ₹39 (b) ₹36 (c) ₹16 (d) ₹72
19. 19.If 7 pens cost ₹168, how much do 10 pens cost? (a) ₹1680 (b) ₹240 (c) ₹171 (d) ₹264
20. 20.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹72 (b) ₹18 (c) ₹126 (d) ₹99
21. 21.If 4 mangoes cost ₹64, how much do 7 mangoes cost? (a) ₹67 (b) ₹112 (c) ₹448 (d) ₹128
22. 22.₹168 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹24 (b) ₹84 (c) ₹168 (d) ₹144
23. 23.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹20 (d) ₹35
24. 24.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 25 days (c) 16 days (d) 5 days
25. 25.If 7 mangoes cost ₹49, how much do 11 mangoes cost? (a) ₹53 (b) ₹539 (c) ₹77 (d) ₹84
26. 26.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 19 days (d) 4 days
27. 27.If 7 kites cost ₹161, how much do 11 kites cost? (a) ₹165 (b) ₹253 (c) ₹1771 (d) ₹276
28. 28.₹55 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹30 (c) ₹25 (d) ₹5
29. 29.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹369 (b) ₹328 (c) ₹205 (d) ₹41
30. 30.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹170 (b) ₹34 (c) ₹153 (d) ₹136
31. 31.₹172 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹129 (b) ₹43 (c) ₹172 (d) ₹86
32. 32.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 15 days (d) 1 day
33. 33.₹56 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹24 (c) ₹32 (d) ₹8
34. 34.If 5 mangoes cost ₹70, how much do 8 mangoes cost? (a) ₹112 (b) ₹126 (c) ₹73 (d) ₹560
35. 35.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹329 (b) ₹141 (c) ₹235 (d) ₹47
36. 36.If 2 mangoes cost ₹16, how much do 8 mangoes cost? (a) ₹72 (b) ₹128 (c) ₹64 (d) ₹22
37. 37.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹92 (b) ₹46 (c) ₹184 (d) ₹138
38. 38.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 10 days (c) 20 days (d) 14 days
39. 39.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹24 (b) ₹120 (c) ₹60 (d) ₹96
40. 40.If 4 mangoes cost ₹60, how much do 10 mangoes cost? (a) ₹165 (b) ₹600 (c) ₹150 (d) ₹66

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