Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 289 · 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.₹494 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹342 (b) ₹152 (c) ₹247 (d) ₹38
2. 2.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹120 (b) ₹160 (c) ₹140 (d) ₹40
3. 3.If 4 notebooks cost ₹60, how much do 8 notebooks cost? (a) ₹120 (b) ₹480 (c) ₹64 (d) ₹135
4. 4.If 9 kites cost ₹198, how much do 11 kites cost? (a) ₹200 (b) ₹242 (c) ₹264 (d) ₹2178
5. 5.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹33 (b) ₹24 (c) ₹42 (d) ₹6
6. 6.If 6 pens cost ₹96, how much do 7 pens cost? (a) ₹97 (b) ₹128 (c) ₹672 (d) ₹112
7. 7.If 9 mangoes cost ₹117, how much do 4 mangoes cost? (a) ₹112 (b) ₹65 (c) ₹52 (d) ₹468
8. 8.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹390 (b) ₹78 (c) ₹39 (d) ₹351
9. 9.If 2 kites cost ₹36, how much do 8 kites cost? (a) ₹288 (b) ₹42 (c) ₹162 (d) ₹144
10. 10.If 8 pens cost ₹72, how much do 9 pens cost? (a) ₹73 (b) ₹648 (c) ₹90 (d) ₹81
11. 11.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
12. 12.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 27 days (d) 3 days
13. 13.₹56 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹16 (b) ₹40 (c) ₹28 (d) ₹8
14. 14.If 9 mangoes cost ₹225, how much do 3 mangoes cost? (a) ₹675 (b) ₹75 (c) ₹100 (d) ₹219
15. 15.₹441 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹393 (b) ₹441 (c) ₹392 (d) ₹49
16. 16.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 36 days (d) 16 days
17. 17.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 13 days (d) 3 days
18. 18.If 2 notebooks cost ₹8, how much do 3 notebooks cost? (a) ₹16 (b) ₹24 (c) ₹12 (d) ₹9
19. 19.If 7 notebooks cost ₹112, how much do 6 notebooks cost? (a) ₹112 (b) ₹111 (c) ₹96 (d) ₹672
20. 20.If 7 kites cost ₹35, how much do 10 kites cost? (a) ₹38 (b) ₹50 (c) ₹350 (d) ₹55
21. 21.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 19 days (d) 7 days
22. 22.If 2 notebooks cost ₹44, how much do 10 notebooks cost? (a) ₹440 (b) ₹52 (c) ₹242 (d) ₹220
23. 23.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹36 (b) ₹288 (c) ₹234 (d) ₹180
24. 24.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 2 days (d) 4 days
25. 25.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 43 days (c) 42 days (d) 10 days
26. 26.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹180 (b) ₹324 (c) ₹252 (d) ₹36
27. 27.If 4 mangoes cost ₹100, how much do 10 mangoes cost? (a) ₹1000 (b) ₹106 (c) ₹250 (d) ₹275
28. 28.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹125 (b) ₹25 (c) ₹150 (d) ₹100
29. 29.If 5 mangoes cost ₹90, how much do 6 mangoes cost? (a) ₹540 (b) ₹126 (c) ₹91 (d) ₹108
30. 30.₹360 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹225 (b) ₹180 (c) ₹45 (d) ₹135
31. 31.If 2 kites cost ₹10, how much do 9 kites cost? (a) ₹90 (b) ₹45 (c) ₹50 (d) ₹17
32. 32.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 24 days (c) 17 days (d) 7 days
33. 33.₹126 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹63 (b) ₹90 (c) ₹18 (d) ₹36
34. 34.If 3 mangoes cost ₹24, how much do 8 mangoes cost? (a) ₹72 (b) ₹29 (c) ₹64 (d) ₹192
35. 35.If 2 pens cost ₹20, how much do 10 pens cost? (a) ₹200 (b) ₹100 (c) ₹110 (d) ₹28
36. 36.If 9 mangoes cost ₹225, how much do 7 mangoes cost? (a) ₹200 (b) ₹175 (c) ₹1575 (d) ₹223
37. 37.If 8 mangoes cost ₹168, how much do 4 mangoes cost? (a) ₹164 (b) ₹672 (c) ₹84 (d) ₹105
38. 38.If 3 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹84 (b) ₹64 (c) ₹252 (d) ₹105
39. 39.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 9 days (d) 4 days
40. 40.₹400 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹400 (b) ₹350 (c) ₹50 (d) ₹200

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