Fractions in Disguise - Exercise 1.4 Class 8 Maths - Chapter 1 NCERT Solutions
NCERT detailed solutions for Class 8 Maths NCERT Ganita Prakash Term 2 Chapter 1, Fractions in Disguise Exercise 1.4, are provided below. These solutions are prepared by the expert team at ALLEN in a simple and easy-to-follow manner, helping students understand the methods used in the exercise and work through the questions effectively for their final exams and future academic learning.Exercise 1.4 is not just calculating percentages, it is about repeated percentage growth and how an amount changes over successive periods. The exercise covers the calculation of updated amount with simple interest and compound interest, interest on previously accumulated interest, comparison of simple and compound interest, and final amount after multiple compoundings.
1.0Download Class 8 Maths Chapter 1 Ex 1.4 NCERT Solutions PDF
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2.0Detailed NCERT Solutions on Fractions in Disguise Exercise 1.4 Class 8 Maths (Ganita Prakashan Term 2)
1. The Bank of Yahapur offers an interest rate of 10% p.a. Compare the amount one earns by depositing ₹20,000 for a period of 2 years with and without compounding annually.
Sol. Without compounding
Amount =P(1+100rt)
=20,000×(1+10010×2)=20,000(1+0.20)
=20,000×1.20=₹24,000
With compounding
Amount =P(1+r)t=20,000×(1+10010)2
=20,000×1.21=₹24,200
Comparison:
Without compounding = ₹24,000
With compounding = ₹24,200
Difference = ₹24,200 - ₹24,000 = ₹200
Hence, with compounding, one gets ₹200 more than without compounding.
2. The Bank of Wahapur offers an interest rate of 5% p.a. Compare the amount one earns by depositing ₹20,000 for a period of 4 years with and without compounding annually.
Sol. P=₹20,000;t=4,r=5
SI=10020000×5×4=₹4,000
A=₹20,000×(1+1005)4
=₹20,000×(2021)4
= ₹ 20,000×2021×2021×2021×2021=₹24310.13
CI=₹24,310.13−₹20,000=₹4,310.13
SI (without compounding) < CI (with compounding)
3. Do you observe anything interesting in the solutions of the two questions above? Share and discuss.
Sol. If the rate percent and time is same, the interest received with compounding is more than the interest received without compounding.
3.0Key Concepts of Chapter 1- Fractions in Disguise Exercise 1.4
- Understanding repeated percentage growth over successive periods.
- Calculating growth when each percentage increase is applied to the updated amount.
- Understanding simple interest and its calculation on the original principal.
- Understanding compound interest when interest is added to the principal for the next period.
- Calculating the amount after repeated compounding.
- Comparing the amounts obtained through simple and compound interest.
- Understanding how accumulated interest contributes to further growth.
4.0Benefits of NCERT Solutions Class 8 Maths Chapter 1 Exercise 1.4
- Explains the calculation of repeated percentage growth on the changing amount.
- Shows how simple interest is calculated using the original principal for each period.
- Clarifies how compound interest is added to the amount before calculating the next period’s interest.
- Breaks down the calculation of interest earned on the previously accumulated interest.
- Shows how to calculate the final amount after successive periods of compounding.
- Helps compare the final amounts obtained through simple and compound interest.
- Explains how repeated compounding changes the overall growth of an amount.