1. The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is $\frac{3}{2}$. Find the rational number.
[3]
2. Arjun is twice as old as Shriya. Five years ago his age was three times Shriya's age. Find their present ages.
[3]
3. The sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?
[3]
4. A steamer goes downstream and covers the distance between two ports in 4 hours while it covers the same distance upstream in 5 hours. If the speed of the stream is $2 \text{ km/hr}$, find the speed of the steamer in still water.
[3]
5. Bansi has 3 times as many 2-rupee coins as he has 5-rupee coins. If he has in all a sum of ₹77, how many coins of each denomination does he have?
[3]
SECTION B: COMPARING QUANTITIES (3 Marks Each)
6. A shopkeeper offers a discount of $10\%$ on the marked price of an article and still makes a profit of $20\%$. If the marked price is ₹1200, find the cost price of the article.
[3]
7. Find the difference between the Compound Interest and Simple Interest on ₹20,000 for 2 years at $8\%$ per annum.
[3]
8. The population of a city was 20,000 in the year 1997. It increased at the rate of $5\%$ p.a. Find the population at the end of the year 2000.
[3]
9. Fabina borrows ₹12,500 at $12\%$ per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at $10\%$ per annum, compounded annually. Who pays more interest and by how much?
[3]
10. A man sold two buffaloes for ₹20,000 each. On one he made a gain of $5\%$ and on the other a loss of $10\%$. Find his overall gain or loss.
[3]
SECTION C: WORK, TIME & DIRECT/INVERSE (3 Marks Each)
11. If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?
[3]
12. A garrison of 120 men has provisions for 30 days. At the end of 5 days, 5 more men joined them. How many days can they sustain on the remaining provision?
[3]
13. A train is moving at a uniform speed of $75 \text{ km/hour}$. (i) How far will it travel in 20 minutes? (ii) Find the time required to cover a distance of 250 km.
[3]
14. A and B together can do a piece of work in 12 days, while B alone can finish it in 30 days. In how many days can A alone finish the work?
[3]
15. A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
[3]
SECTION D: MENSURATION (3 Marks Each)
16. A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area 1080 sq. m?
[3]
17. A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.
[3]
18. A rectangular piece of paper 11 cm x 4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder.
[3]
19. A godown is in the form of a cuboid of measures $60\text{m} \times 40\text{m} \times 30\text{m}$. How many cuboidal boxes can be stored in it if the volume of one box is $0.8 \text{ m}^3$?
[3]
20. The parallel sides of a trapezium are 20m and 30m and its non-parallel sides are 6m and 8m. Find the area of the trapezium.
[3]
SECTION E: HIGH ORDER THINKING SKILLS (4 Marks Each)
21. A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain the same. Find the minimum number of plants he needs more for this.
[4]
22. Evaluate using laws of exponents: find the value of $x$ if: $5^{2x+1} \div 25 = 125$
[4]
23. Find the smallest number by which 675 must be multiplied so that the product is a perfect cube. Also find the cube root of the product.
[4]
24. Three numbers are in the ratio 2:3:4. The sum of their cubes is 33957. Find the numbers.
[4]
25. The adjacent angles of a parallelogram are in the ratio 2:3. Find all the angles of the parallelogram.
