Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 266 · 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.₹372 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹186 (b) ₹217 (c) ₹31 (d) ₹155
2. 2.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹275 (b) ₹50 (c) ₹350 (d) ₹200
3. 3.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹96 (b) ₹72 (c) ₹84 (d) ₹24
4. 4.If 3 kites cost ₹72, how much do 7 kites cost? (a) ₹168 (b) ₹504 (c) ₹192 (d) ₹76
5. 5.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹70 (b) ₹10 (c) ₹50 (d) ₹90
6. 6.If 6 mangoes cost ₹120, how much do 3 mangoes cost? (a) ₹117 (b) ₹360 (c) ₹60 (d) ₹80
7. 7.₹400 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹200 (b) ₹150 (c) ₹50 (d) ₹250
8. 8.If 2 pens cost ₹30, how much do 9 pens cost? (a) ₹37 (b) ₹135 (c) ₹270 (d) ₹150
9. 9.₹340 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹170 (b) ₹102 (c) ₹238 (d) ₹34
10. 10.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 13 days
11. 11.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹117 (b) ₹26 (c) ₹130 (d) ₹104
12. 12.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹238 (b) ₹34 (c) ₹204 (d) ₹170
13. 13.If 2 pens cost ₹12, how much do 5 pens cost? (a) ₹36 (b) ₹30 (c) ₹60 (d) ₹15
14. 14.₹203 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹87 (b) ₹29 (c) ₹145 (d) ₹116
15. 15.If 2 mangoes cost ₹20, how much do 7 mangoes cost? (a) ₹70 (b) ₹140 (c) ₹80 (d) ₹25
16. 16.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 6 days (d) 14 days
17. 17.If 9 kites cost ₹198, how much do 10 kites cost? (a) ₹242 (b) ₹1980 (c) ₹220 (d) ₹199
18. 18.If 8 notebooks cost ₹200, how much do 9 notebooks cost? (a) ₹201 (b) ₹225 (c) ₹1800 (d) ₹250
19. 19.If 5 notebooks cost ₹50, how much do 6 notebooks cost? (a) ₹300 (b) ₹51 (c) ₹70 (d) ₹60
20. 20.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹6 (c) ₹12 (d) ₹18
21. 21.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 7 days (d) 15 days
22. 22.If 6 notebooks cost ₹114, how much do 10 notebooks cost? (a) ₹209 (b) ₹190 (c) ₹1140 (d) ₹118
23. 23.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹17 (b) ₹119 (c) ₹102 (d) ₹85
24. 24.₹550 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹50 (b) ₹100 (c) ₹450 (d) ₹275
25. 25.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹360 (b) ₹200 (c) ₹280 (d) ₹40
26. 26.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹80 (b) ₹104 (c) ₹16 (d) ₹128
27. 27.If 4 pens cost ₹68, how much do 5 pens cost? (a) ₹69 (b) ₹102 (c) ₹340 (d) ₹85
28. 28.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 9 days (c) 17 days (d) 26 days
29. 29.If 2 kites cost ₹38, how much do 10 kites cost? (a) ₹46 (b) ₹190 (c) ₹380 (d) ₹209
30. 30.₹115 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹23 (b) ₹46 (c) ₹69 (d) ₹92
31. 31.If 7 notebooks cost ₹35, how much do 5 notebooks cost? (a) ₹25 (b) ₹33 (c) ₹175 (d) ₹30
32. 32.If 8 mangoes cost ₹32, how much do 12 mangoes cost? (a) ₹384 (b) ₹36 (c) ₹52 (d) ₹48
33. 33.If 3 pens cost ₹24, how much do 4 pens cost? (a) ₹32 (b) ₹96 (c) ₹25 (d) ₹40
34. 34.₹140 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹70 (b) ₹28 (c) ₹112 (d) ₹140
35. 35.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 11 days (d) 17 days
36. 36.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 18 days (d) 4 days
37. 37.If 9 kites cost ₹117, how much do 10 kites cost? (a) ₹118 (b) ₹1170 (c) ₹143 (d) ₹130
38. 38.If 4 notebooks cost ₹52, how much do 11 notebooks cost? (a) ₹143 (b) ₹572 (c) ₹59 (d) ₹156
39. 39.If 5 mangoes cost ₹40, how much do 9 mangoes cost? (a) ₹72 (b) ₹44 (c) ₹360 (d) ₹80
40. 40.₹364 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹182 (b) ₹234 (c) ₹130 (d) ₹26

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