Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 491 · 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 ₹14, how much do 7 mangoes cost? (a) ₹98 (b) ₹19 (c) ₹56 (d) ₹49
2. 2.If 4 mangoes cost ₹64, how much do 5 mangoes cost? (a) ₹320 (b) ₹65 (c) ₹80 (d) ₹96
3. 3.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 22 days (c) 15 days (d) 21 days
4. 4.If 8 pens cost ₹48, how much do 3 pens cost? (a) ₹144 (b) ₹24 (c) ₹43 (d) ₹18
5. 5.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 13 days (d) 10 days
6. 6.₹403 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹124 (b) ₹279 (c) ₹310 (d) ₹31
7. 7.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 13 days (d) 16 days
8. 8.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 5 days (d) 6 days
9. 9.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹78 (b) ₹65 (c) ₹26 (d) ₹13
10. 10.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹135 (b) ₹243 (c) ₹27 (d) ₹216
11. 11.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹234 (b) ₹195 (c) ₹39 (d) ₹273
12. 12.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹432 (b) ₹48 (c) ₹96 (d) ₹264
13. 13.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹32 (c) ₹8 (d) ₹20
14. 14.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹10 (b) ₹35 (c) ₹20 (d) ₹50
15. 15.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 4 days (d) 16 days
16. 16.If 2 kites cost ₹12, how much do 10 kites cost? (a) ₹66 (b) ₹120 (c) ₹60 (d) ₹20
17. 17.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹84 (b) ₹49 (c) ₹14 (d) ₹98
18. 18.If 7 notebooks cost ₹140, how much do 8 notebooks cost? (a) ₹180 (b) ₹1120 (c) ₹160 (d) ₹141
19. 19.If 9 kites cost ₹63, how much do 4 kites cost? (a) ₹58 (b) ₹252 (c) ₹35 (d) ₹28
20. 20.If 4 kites cost ₹64, how much do 5 kites cost? (a) ₹320 (b) ₹80 (c) ₹65 (d) ₹96
21. 21.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹31 (b) ₹217 (c) ₹248 (d) ₹124
22. 22.₹243 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹217 (b) ₹216 (c) ₹27 (d) ₹243
23. 23.If 3 kites cost ₹36, how much do 4 kites cost? (a) ₹144 (b) ₹60 (c) ₹37 (d) ₹48
24. 24.If 5 mangoes cost ₹85, how much do 6 mangoes cost? (a) ₹102 (b) ₹86 (c) ₹510 (d) ₹119
25. 25.₹460 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹46 (b) ₹414 (c) ₹230 (d) ₹460
26. 26.If 6 pens cost ₹36, how much do 12 pens cost? (a) ₹42 (b) ₹432 (c) ₹72 (d) ₹78
27. 27.If 7 mangoes cost ₹161, how much do 3 mangoes cost? (a) ₹69 (b) ₹92 (c) ₹157 (d) ₹483
28. 28.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 8 days (d) 7 days
29. 29.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 7 days (d) 9 days
30. 30.If 2 notebooks cost ₹16, how much do 6 notebooks cost? (a) ₹48 (b) ₹20 (c) ₹96 (d) ₹56
31. 31.If 2 notebooks cost ₹40, how much do 6 notebooks cost? (a) ₹240 (b) ₹120 (c) ₹44 (d) ₹140
32. 32.If 7 pens cost ₹49, how much do 8 pens cost? (a) ₹392 (b) ₹50 (c) ₹63 (d) ₹56
33. 33.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 25 days (d) 5 days
34. 34.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 19 days (c) 18 days (d) 11 days
35. 35.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 28 days (d) 17 days
36. 36.₹93 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹63 (b) ₹62 (c) ₹93 (d) ₹31
37. 37.If 3 mangoes cost ₹12, how much do 4 mangoes cost? (a) ₹48 (b) ₹20 (c) ₹13 (d) ₹16
38. 38.If 4 pens cost ₹80, how much do 7 pens cost? (a) ₹560 (b) ₹83 (c) ₹160 (d) ₹140
39. 39.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹240 (b) ₹40 (c) ₹280 (d) ₹140
40. 40.If 5 pens cost ₹110, how much do 9 pens cost? (a) ₹198 (b) ₹114 (c) ₹990 (d) ₹220

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