Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 145 · 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 4 notebooks cost ₹16, how much do 3 notebooks cost? (a) ₹48 (b) ₹16 (c) ₹15 (d) ₹12
2. 2.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹15 (b) ₹10 (c) ₹20 (d) ₹5
3. 3.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 28 days (d) 7 days
4. 4.₹406 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹203 (b) ₹261 (c) ₹145 (d) ₹29
5. 5.If 7 kites cost ₹154, how much do 5 kites cost? (a) ₹132 (b) ₹110 (c) ₹770 (d) ₹152
6. 6.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 18 days (d) 8 days
7. 7.If 7 mangoes cost ₹84, how much do 2 mangoes cost? (a) ₹168 (b) ₹79 (c) ₹36 (d) ₹24
8. 8.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹80 (b) ₹45 (c) ₹90 (d) ₹10
9. 9.If 5 pens cost ₹40, how much do 6 pens cost? (a) ₹240 (b) ₹56 (c) ₹41 (d) ₹48
10. 10.If 7 pens cost ₹161, how much do 5 pens cost? (a) ₹159 (b) ₹115 (c) ₹138 (d) ₹805
11. 11.₹84 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹24 (b) ₹60 (c) ₹12 (d) ₹42
12. 12.₹370 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹333 (b) ₹37 (c) ₹370 (d) ₹185
13. 13.If 9 mangoes cost ₹90, how much do 3 mangoes cost? (a) ₹270 (b) ₹30 (c) ₹40 (d) ₹84
14. 14.If 3 mangoes cost ₹66, how much do 2 mangoes cost? (a) ₹66 (b) ₹65 (c) ₹132 (d) ₹44
15. 15.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 15 days (d) 14 days
16. 16.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹112 (d) ₹126
17. 17.If 7 mangoes cost ₹28, how much do 8 mangoes cost? (a) ₹36 (b) ₹32 (c) ₹29 (d) ₹224
18. 18.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 3 days (d) 27 days
19. 19.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 19 days (d) 17 days
20. 20.₹360 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹180 (b) ₹108 (c) ₹252 (d) ₹36
21. 21.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹175 (c) ₹35 (d) ₹140
22. 22.If 9 pens cost ₹216, how much do 4 pens cost? (a) ₹96 (b) ₹120 (c) ₹864 (d) ₹211
23. 23.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 21 days (d) 20 days
24. 24.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 4 days (d) 8 days
25. 25.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 23 days (d) 24 days
26. 26.If 4 mangoes cost ₹100, how much do 5 mangoes cost? (a) ₹500 (b) ₹150 (c) ₹101 (d) ₹125
27. 27.₹176 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹110 (b) ₹22 (c) ₹66 (d) ₹88
28. 28.If 4 notebooks cost ₹88, how much do 11 notebooks cost? (a) ₹968 (b) ₹95 (c) ₹242 (d) ₹264
29. 29.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 11 days
30. 30.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 37 days (c) 15 days (d) 36 days
31. 31.If 6 pens cost ₹144, how much do 11 pens cost? (a) ₹1584 (b) ₹149 (c) ₹264 (d) ₹288
32. 32.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹60 (b) ₹25 (c) ₹16 (d) ₹20
33. 33.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹221 (d) ₹272
34. 34.₹308 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹88 (b) ₹44 (c) ₹154 (d) ₹220
35. 35.If 2 pens cost ₹12, how much do 6 pens cost? (a) ₹36 (b) ₹16 (c) ₹42 (d) ₹72
36. 36.₹243 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹27 (b) ₹54 (c) ₹216 (d) ₹189
37. 37.If 6 mangoes cost ₹102, how much do 7 mangoes cost? (a) ₹714 (b) ₹103 (c) ₹119 (d) ₹136
38. 38.If 7 pens cost ₹119, how much do 8 pens cost? (a) ₹120 (b) ₹136 (c) ₹952 (d) ₹153
39. 39.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 2 days (d) 9 days
40. 40.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 5 days (d) 4 days

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