30 Mathematic for Madrasa Service Commission Group D Recruitment

30 Mathematic for Madrasa Service Commission Group D Recruitment

1. Problem: Simplify $45 \div 9 + 3 \times 6 - 4$.

• Solution: $45 \div 9 + 3 \times 6 - 4 = 5 + 18 - 4 = 19$.

2. Problem: Find the LCM of 12, 15, and 20.

• Solution: $\text{LCM of } 12, 15, 20 = 60$.

3. Problem: Solve for $x$ if $3x - 5 = 16$.

• Solution: $3x = 21$ $\Rightarrow x = 7$.

4. Problem: Simplify $\frac{5}{8} + \frac{3}{4}$.

• Solution: $\frac{5}{8} + \frac{6}{8} = \frac{11}{8}$.

5. Problem: Convert $0.75$ to a fraction.

• Solution: $0.75 = \frac{3}{4}$.

6. Problem: Find the value of $25\%$ of 240.

• Solution: $25\%$ of 240 $= \frac{25}{100} \times 240 = 60$.

7. Problem: What is the simple interest on Rs. 1000 at $5\%$ per annum for 2 years?

• Solution: $\text{SI} = \frac{1000 \times 5 \times 2}{100} = Rs. 100$.

8. Problem: Solve $2x + 3 = 7$.

• Solution: $2x = 4$ $\Rightarrow x = 2$.

9. Problem: What is the sum of the first 10 natural numbers?

• Solution: $S = \frac{n(n+1)}{2} = \frac{10(10+1)}{2} = 55$.

10. Problem: Find the area of a rectangle with length 12 cm and width 8 cm.

• Solution: $\text{Area} = \text{Length} \times \text{Width} = 12 \times 8 = 96 \, \text{cm}^2$.

11. Problem: Convert $\frac{7}{20}$ to a percentage.

• Solution: $\frac{7}{20} \times 100 = 35\%$.

12. Problem: Find the HCF of 48 and 64.

• Solution: $\text{HCF of } 48 \text{ and } 64 = 16$.

13. Problem: Solve $4x - 7 = 2x + 5$.

• Solution: $2x = 12$ $\Rightarrow x = 6$.

14. Problem: Simplify $2(3x + 4) - 5x$.

• Solution: $6x + 8 - 5x = x + 8$.

15. Problem: What is $15\%$ of Rs. 500?

• Solution: $\frac{15}{100} \times 500 = Rs. 75$.

16. Problem: Find the value of $5 \times (4 + 3) \div 7$.

• Solution: $5 \times 7 \div 7 = 5$.

17. Problem: A man bought a TV for Rs. 15,000 and sold it for Rs. 18,000. What is his profit percentage?

• Solution: $\text{Profit} = \frac{3000}{15000} \times 100 = 20\%$.

18. Problem: Calculate the average of the numbers 7, 14, 21, and 28.

• Solution: $\text{Average} = \frac{7+14+21+28}{4} = 17.5$.

19. Problem: A sum of Rs. 500 is divided among A, B, and C in the ratio 2:3:5. What is B's share?

• Solution: $\text{B's share} = \frac{3}{10} \times 500 = Rs. 150$.

20. Problem: Solve $\frac{2}{3}x + 5 = 11$.

• Solution: $\frac{2}{3}x = 6$ $\Rightarrow x = 9$.

21. Problem: What is the perimeter of a square with side 6 cm?

• Solution: $\text{Perimeter} = 4 \times 6 = 24 \, \text{cm}$.

22. Problem: Simplify $3 \times 4 + 8 \div 2$.

• Solution: $12 + 4 = 16$.

23. Problem: Convert $2.5$ hours to minutes.

• Solution: $2.5 \times 60 = 150$ minutes.

24. Problem: A car travels 60 km in 1.5 hours. What is its speed in km/h?

• Solution: $\text{Speed} = \frac{60}{1.5} = 40 \, \text{km/h}$.

25. Problem: Solve $7x + 2 = 30$.

• Solution: $7x = 28$ $\Rightarrow x = 4$.

26. Problem: Find the area of a triangle with base 10 cm and height 12 cm.

• Solution: $\text{Area} = \frac{1}{2} \times 10 \times 12 = 60 \, \text{cm}^2$.

27. Problem: What is $75\%$ of 80?

• Solution: $75\%$ of 80 $= \frac{75}{100} \times 80 = 60$.

28. Problem: If the cost price of an article is Rs. 500 and the selling price is Rs. 550, find the profit percentage.

• Solution: $\text{Profit} = \frac{50}{500} \times 100 = 10\%$.

29. Problem: Convert $\frac{1}{5}$ to a decimal.

• Solution: $\frac{1}{5} = 0.2$.

30. Problem: Find the ratio of 45 minutes to 1.5 hours.

• Solution: $\text{Ratio} = \frac{45}{90} = 1:2$.