Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 842 · 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 5 pens cost ₹85, how much do 6 pens cost? (a) ₹102 (b) ₹510 (c) ₹119 (d) ₹86
2. 2.If 5 kites cost ₹25, how much do 4 kites cost? (a) ₹100 (b) ₹20 (c) ₹25 (d) ₹24
3. 3.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 7 days
4. 4.If 4 notebooks cost ₹40, how much do 10 notebooks cost? (a) ₹46 (b) ₹100 (c) ₹400 (d) ₹110
5. 5.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 7 days
6. 6.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 6 days (d) 14 days
7. 7.If 3 mangoes cost ₹75, how much do 4 mangoes cost? (a) ₹100 (b) ₹76 (c) ₹125 (d) ₹300
8. 8.If 8 pens cost ₹40, how much do 7 pens cost? (a) ₹35 (b) ₹280 (c) ₹39 (d) ₹40
9. 9.₹48 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹48 (d) ₹24
10. 10.₹96 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹48 (c) ₹12 (d) ₹60
11. 11.If 3 mangoes cost ₹57, how much do 4 mangoes cost? (a) ₹76 (b) ₹228 (c) ₹58 (d) ₹95
12. 12.If 3 pens cost ₹69, how much do 5 pens cost? (a) ₹115 (b) ₹71 (c) ₹345 (d) ₹138
13. 13.If 7 kites cost ₹49, how much do 4 kites cost? (a) ₹35 (b) ₹46 (c) ₹28 (d) ₹196
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. 15.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 1 day (d) 8 days
16. 16.₹481 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹296 (b) ₹333 (c) ₹185 (d) ₹37
17. 17.If 8 notebooks cost ₹176, how much do 2 notebooks cost? (a) ₹66 (b) ₹44 (c) ₹170 (d) ₹352
18. 18.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 11 days (d) 2 days
19. 19.If 5 mangoes cost ₹85, how much do 10 mangoes cost? (a) ₹850 (b) ₹170 (c) ₹90 (d) ₹187
20. 20.If 3 notebooks cost ₹27, how much do 11 notebooks cost? (a) ₹108 (b) ₹297 (c) ₹99 (d) ₹35
21. 21.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 8 days (d) 6 days
22. 22.If 6 notebooks cost ₹48, how much do 8 notebooks cost? (a) ₹72 (b) ₹50 (c) ₹64 (d) ₹384
23. 23.If 3 mangoes cost ₹60, how much do 4 mangoes cost? (a) ₹240 (b) ₹61 (c) ₹100 (d) ₹80
24. 24.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 13 days (d) 21 days
25. 25.If 8 mangoes cost ₹136, how much do 3 mangoes cost? (a) ₹408 (b) ₹131 (c) ₹68 (d) ₹51
26. 26.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 25 days (d) 17 days
27. 27.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 9 days (d) 6 days
28. 28.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 15 days (d) 1 day
29. 29.₹304 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹38 (b) ₹152 (c) ₹190 (d) ₹114
30. 30.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹25 (c) ₹40 (d) ₹5
31. 31.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 28 days (d) 18 days
32. 32.If 5 kites cost ₹125, how much do 10 kites cost? (a) ₹250 (b) ₹1250 (c) ₹275 (d) ₹130
33. 33.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 10 days (d) 4 days
34. 34.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹36 (b) ₹144 (c) ₹180 (d) ₹162
35. 35.If 4 pens cost ₹12, how much do 5 pens cost? (a) ₹15 (b) ₹13 (c) ₹18 (d) ₹60
36. 36.If 8 mangoes cost ₹32, how much do 9 mangoes cost? (a) ₹36 (b) ₹40 (c) ₹33 (d) ₹288
37. 37.If 7 kites cost ₹42, how much do 4 kites cost? (a) ₹30 (b) ₹39 (c) ₹168 (d) ₹24
38. 38.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 15 days (d) 6 days
39. 39.If 5 kites cost ₹45, how much do 9 kites cost? (a) ₹90 (b) ₹81 (c) ₹405 (d) ₹49
40. 40.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 7 days (c) 19 days (d) 39 days

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