Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 978 · 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. 1.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 5 days (d) 4 days
2. 2.If 3 mangoes cost ₹9, how much do 12 mangoes cost? (a) ₹108 (b) ₹39 (c) ₹36 (d) ₹18
3. 3.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹70 (b) ₹30 (c) ₹50 (d) ₹10
4. 4.If 4 mangoes cost ₹36, how much do 5 mangoes cost? (a) ₹37 (b) ₹180 (c) ₹54 (d) ₹45
5. 5.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 21 days (d) 22 days
6. 6.₹143 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹104 (b) ₹39 (c) ₹13 (d) ₹117
7. 7.If 2 notebooks cost ₹8, how much do 9 notebooks cost? (a) ₹72 (b) ₹36 (c) ₹15 (d) ₹40
8. 8.₹96 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹60 (b) ₹12 (c) ₹48 (d) ₹36
9. 9.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹84 (b) ₹14 (c) ₹49 (d) ₹98
10. 10.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹105 (b) ₹90 (c) ₹75 (d) ₹15
11. 11.If 3 notebooks cost ₹9, how much do 12 notebooks cost? (a) ₹18 (b) ₹39 (c) ₹36 (d) ₹108
12. 12.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹245 (c) ₹210 (d) ₹175
13. 13.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 2 days (d) 6 days
14. 14.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹48 (b) ₹240 (c) ₹336 (d) ₹288
15. 15.If 9 kites cost ₹45, how much do 2 kites cost? (a) ₹90 (b) ₹15 (c) ₹38 (d) ₹10
16. 16.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 26 days (d) 27 days
17. 17.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 40 days (c) 39 days (d) 7 days
18. 18.If 3 notebooks cost ₹12, how much do 8 notebooks cost? (a) ₹32 (b) ₹36 (c) ₹96 (d) ₹17
19. 19.If 7 mangoes cost ₹35, how much do 11 mangoes cost? (a) ₹385 (b) ₹39 (c) ₹60 (d) ₹55
20. 20.If 9 mangoes cost ₹135, how much do 10 mangoes cost? (a) ₹1350 (b) ₹136 (c) ₹150 (d) ₹165
21. 21.If 7 mangoes cost ₹161, how much do 6 mangoes cost? (a) ₹966 (b) ₹160 (c) ₹161 (d) ₹138
22. 22.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹315 (b) ₹45 (c) ₹225 (d) ₹270
23. 23.If 5 kites cost ₹85, how much do 7 kites cost? (a) ₹87 (b) ₹119 (c) ₹595 (d) ₹136
24. 24.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 23 days (c) 5 days (d) 45 days
25. 25.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹36 (b) ₹66 (c) ₹96 (d) ₹12
26. 26.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 13 days (d) 14 days
27. 27.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 13 days (d) 12 days
28. 28.₹416 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹128 (b) ₹32 (c) ₹288 (d) ₹208
29. 29.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹228 (b) ₹190 (c) ₹209 (d) ₹38
30. 30.₹252 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹36 (b) ₹180 (c) ₹72 (d) ₹126
31. 31.If 7 pens cost ₹140, how much do 5 pens cost? (a) ₹138 (b) ₹100 (c) ₹700 (d) ₹120
32. 32.₹336 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹48 (b) ₹336 (c) ₹168 (d) ₹288
33. 33.If 5 mangoes cost ₹85, how much do 9 mangoes cost? (a) ₹89 (b) ₹153 (c) ₹765 (d) ₹170
34. 34.If 9 kites cost ₹36, how much do 6 kites cost? (a) ₹28 (b) ₹216 (c) ₹24 (d) ₹33
35. 35.If 2 notebooks cost ₹20, how much do 10 notebooks cost? (a) ₹110 (b) ₹28 (c) ₹200 (d) ₹100
36. 36.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 28 days (c) 3 days (d) 27 days
37. 37.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹28 (b) ₹126 (c) ₹112 (d) ₹140
38. 38.₹252 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹42 (b) ₹252 (c) ₹210 (d) ₹126
39. 39.If 6 pens cost ₹54, how much do 7 pens cost? (a) ₹63 (b) ₹72 (c) ₹378 (d) ₹55
40. 40.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 63 days (b) 21 days (c) 7 days (d) 64 days

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