Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 368 · 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 2 mangoes cost ₹10, how much do 4 mangoes cost? (a) ₹40 (b) ₹20 (c) ₹25 (d) ₹12
2. 2.If 8 pens cost ₹80, how much do 11 pens cost? (a) ₹880 (b) ₹110 (c) ₹120 (d) ₹83
3. 3.If 3 mangoes cost ₹24, how much do 10 mangoes cost? (a) ₹31 (b) ₹240 (c) ₹80 (d) ₹88
4. 4.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹46 (b) ₹184 (c) ₹207 (d) ₹230
5. 5.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 3 days
6. 6.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹80 (b) ₹40 (c) ₹60 (d) ₹120
7. 7.If 2 kites cost ₹32, how much do 6 kites cost? (a) ₹112 (b) ₹36 (c) ₹96 (d) ₹192
8. 8.If 9 pens cost ₹90, how much do 6 pens cost? (a) ₹540 (b) ₹70 (c) ₹87 (d) ₹60
9. 9.₹185 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹37 (b) ₹74 (c) ₹111 (d) ₹148
10. 10.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 49 days (d) 9 days
11. 11.If 9 pens cost ₹198, how much do 11 pens cost? (a) ₹200 (b) ₹242 (c) ₹2178 (d) ₹264
12. 12.If 7 mangoes cost ₹147, how much do 8 mangoes cost? (a) ₹1176 (b) ₹168 (c) ₹148 (d) ₹189
13. 13.₹264 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹165 (b) ₹99 (c) ₹132 (d) ₹33
14. 14.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 28 days (c) 18 days (d) 7 days
15. 15.If 9 notebooks cost ₹63, how much do 12 notebooks cost? (a) ₹91 (b) ₹84 (c) ₹756 (d) ₹66
16. 16.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹44 (b) ₹22 (c) ₹11 (d) ₹33
17. 17.If 5 kites cost ₹80, how much do 8 kites cost? (a) ₹128 (b) ₹83 (c) ₹144 (d) ₹640
18. 18.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹15 (b) ₹120 (c) ₹105 (d) ₹30
19. 19.If 3 notebooks cost ₹57, how much do 8 notebooks cost? (a) ₹171 (b) ₹152 (c) ₹456 (d) ₹62
20. 20.₹176 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹88 (b) ₹132 (c) ₹44 (d) ₹176
21. 21.If 7 mangoes cost ₹112, how much do 10 mangoes cost? (a) ₹115 (b) ₹1120 (c) ₹176 (d) ₹160
22. 22.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 4 days (d) 3 days
23. 23.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 25 days (d) 13 days
24. 24.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹48 (b) ₹16 (c) ₹88 (d) ₹128
25. 25.₹611 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹47 (b) ₹423 (c) ₹470 (d) ₹188
26. 26.If 2 pens cost ₹36, how much do 8 pens cost? (a) ₹144 (b) ₹288 (c) ₹162 (d) ₹42
27. 27.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹136 (d) ₹119
28. 28.If 9 pens cost ₹108, how much do 2 pens cost? (a) ₹101 (b) ₹36 (c) ₹216 (d) ₹24
29. 29.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 11 days
30. 30.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹66 (b) ₹55 (c) ₹11 (d) ₹77
31. 31.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 5 days (d) 4 days
32. 32.₹280 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹252 (b) ₹140 (c) ₹280 (d) ₹28
33. 33.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹48 (c) ₹96 (d) ₹72
34. 34.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 7 days (c) 19 days (d) 53 days
35. 35.₹147 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹49 (b) ₹147 (c) ₹99 (d) ₹98
36. 36.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹290 (b) ₹261 (c) ₹29 (d) ₹145
37. 37.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 16 days (d) 15 days
38. 38.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 8 days (d) 2 days
39. 39.₹200 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹100 (b) ₹140 (c) ₹20 (d) ₹60
40. 40.If 9 notebooks cost ₹153, how much do 7 notebooks cost? (a) ₹136 (b) ₹119 (c) ₹1071 (d) ₹151

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