AIOU Solved Assignments Code 247 (Mathematics - I)

AIOU Solved Assignments Code 247

Spring 2023 Edition

Why AIOU Solved Assignments Matter

Solved assignments provide a structured roadmap to tackle challenging problems, aiding students in achieving academic success while preparing them for exams.

Overview of Code 247

Mathematics – I under Code 247 focuses on fundamental concepts such as algebra and geometry, essential for students across diverse academic fields.

Benefits of Using Solved Assignments

• Provides clarity on complex concepts.
• Saves time with ready-to-use examples.
• Aligns well with exam preparation needs.

Assignment Title: 247 Assignment 1 Total Questions: 5 Q1 (10 Marks) (a) Calculate Ushr on a rice crop by natural resources amounting to Rs. 9,30,000. Solution: Ushr is applicable at the rate of 10% for crops irrigated by natural resources. Ushr = (10 / 100) × Rs. 9,30,000 = Rs. 93,000 (b) Calculate Zakat on gold amounting to Rs. 13,50,000. Solution: Zakat is applicable at the rate of 2.5% on the total value of gold. Zakat = (2.5 / 100) × Rs. 13,50,000 = Rs. 33,750 Q2 (10 Marks) (a) If the stay of 12 men for 7 days in a hotel costs Rs. 20,500, find the cost for the stay of 10 men for 8 days. Solution: Cost is proportional to the number of men and the number of days. Cost per man per day = Rs. 20,500 ÷ (12 × 7) = Rs. 244.05 Cost for 10 men for 8 days = Rs. 244.05 × 10 × 8 = Rs. 19,524 (b) Two angles in a triangle are 45° and 75°. Find the ratio of the third angle to the sum of the first two angles. Solution: Third angle = 180° − (45° + 75°) = 60° Sum of first two angles = 45° + 75° = 120° Ratio = Third angle : Sum of first two angles = 60 : 120 = 1 : 2 Q3 (10 Marks) (a) The marked price of a wall clock is Rs. 900. The shopkeeper offers a discount of 5% and still gains 10%. Find the price at which the shopkeeper purchased it. Solution: Selling price after 5% discount = 95% of Rs. 900 = Rs. 855 Cost price = Selling price ÷ (1 + Gain%) = Rs. 855 ÷ 1.1 = Rs. 777.27 (b) Divide Rs. 18,400 among three friends such that the ratio of their parts is 3:6:8. Solution: Total parts = 3 + 6 + 8 = 17 Friend 1's share = (3 / 17) × Rs. 18,400 = Rs. 3,247.06 Friend 2's share = (6 / 17) × Rs. 18,400 = Rs. 6,494.12 Friend 3's share = (8 / 17) × Rs. 18,400 = Rs. 8,658.82 Q4 (10 Marks) (a) At what annual rate of profit would a sum of Rs. 780 increase to Rs. 1,340 in 2 years 3 months? Solution: Profit = Rs. 1,340 − Rs. 780 = Rs. 560 Time = 2 years 3 months = 2.25 years Rate = (Profit ÷ Principal × 100) ÷ Time = (Rs. 560 ÷ Rs. 780 × 100) ÷ 2.25 = 32.02% (b) Find the compound profit on Rs. 3,000 for 2 years at 4%. Solution: Use the compound interest formula: CI = Principal × [(1 + Rate / 100)^Time − 1] CI = Rs. 3,000 × [(1 + 4 / 100)^2 − 1] CI = Rs. 3,000 × (1.0816 − 1) = Rs. 244.80 Q5 (10 Marks) (a) The price of a motorcycle is Rs. 4,000. If 9% sales tax is charged, calculate the amount of sales tax on 25 such motorcycles. Solution: Sales tax per motorcycle = (9 / 100) × Rs. 4,000 = Rs. 360 Sales tax on 25 motorcycles = Rs. 360 × 25 = Rs. 9,000 (b) If gross pay of a person is Rs. 6,50,000, calculate his net take-home salary after deductions. Solution: Total deductions = Rs. 380 (income tax) + Rs. 700 (benevolent fund) + Rs. 2,100 (G.P. fund) + Rs. 250 (group insurance) = Rs. 3,430 Net salary = Gross pay − Total deductions = Rs. 6,50,000 − Rs. 3,430 = Rs. 6,46,570

10 Marks