**Chapter 6 Financial Planning Practice Set 6.1**

Chapter 6 Financial Planning Practice Set 6.1

**Question 1.Alka spends 90% of the money that she receives every month, and saves â‚¹ 120. How much money does she get monthly?Solution:**

Let Alkaâ€™s monthly income be â‚¹ x.

Alka spends 90% of the money that she receives every month.

âˆ´ Amount spent by Alka = 90% of x

Now, Savings = Income â€“ Expenditure

âˆ´ 120 = x â€“ 0.9x

âˆ´120 = 0.1 x

âˆ´ x = 1200

Alka gets â‚¹ 1200 monthly.

**Question 2.Sumit borrowed a capital of â‚¹ 50,000 to start his food products business. In the first year he suffered a loss of 20%. He invested the remaining capital in a new sweets business and made a profit of 5%. How much was his profit or loss computed on his original capital ?Solution:**

Original capital borrowed by Sumit = â‚¹ 50000

Sumit suffered a loss of 20% in his food products business.

âˆ´ Loss suffered in the first year = 20% of 50000

= â‚¹10000

Remaining capital = Original capital â€“ loss suffered = 50000- 10000

= â‚¹ 40000

Sumit invested the remaining capital i.e. â‚¹ 40,000 in a new sweets business. He made a profit of 5%.

Profit in sweets business = 5% of 40000

= â‚¹ 2000

New capital with Sumit after the profit in new sweets business = 40000 + 2000 = â‚¹42000

Since, the new capital is less than the original capital, we can conclude that Sumit suffered a loss.

Total loss on original capital = Original capital â€“ New capital

= 50000 â€“ 42000 = â‚¹ 8000

âˆ´ Sumit suffered a loss of 16% on the original capital.

Question 3.

Nikhil spent 5% of his monthly income on his childrenâ€™s education, invested 14% in shares, deposited 3% in a bank and used 40% for his daily expenses. He was left with a balance of â‚¹ 19,000. What was his income that month?

Solution:

Let the monthly income of Nikhil be â‚¹ x.

Nikhil invested 14% in shares and deposited 3% in a bank.

âˆ´ Total investment = (14% + 3%) of x

= 17% of x

= 0.1 7 x

Nikhil spent 5% on his childrenâ€™s education and used 40% for his daily expenses.

âˆ´ Total expenditure = (5% + 40%) of x

= 45% of x

= 0.45x

Amount left with Nikhil = 19,000

Amount left with Nikhil = Income â€“ (Total investment + Total expenditure)

âˆ´ 19000 = x â€“ (0.17x + 0.45x)

âˆ´ 19000 = x â€“ 0.62x ,

âˆ´ 19000 = 0.38x

= 50000

âˆ´ The monthly income of Nikhil is â‚¹ 50000.

**Question 4.Mr. Sayyad kept â‚¹ 40,000 in a bank at 8% compound interest for 2 years. Mr. Fernandes invested â‚¹ 1,20,000 in a mutual fund for 2 years. After 2 years, Mr. Fernandes got â‚¹ 1,92,000. Whose investment turned out to be more profitable?Solution:**

Mr. Sayyad:

Mr. Sayyad kept â‚¹ 40,000 in a bank at 8% compound interest for 2 years P = â‚¹ 40000, R = 8%, n = 2 years

âˆ´ Compound interest (I)

= Amount (A) â€“ Principal (P)

= 40000 [(1 +0.08)

^{2}â€“ 1]

= 40000 [(1.08)

^{2}â€“ 1]

= 40000(1.1664 â€“ 1)

= 40000 (0.1664)

= â‚¹ 6656

âˆ´ Mr. Sayyadâ€™s percentage of profit Interest

Mr. Fernandes:

Amount invested by Mr. Fernandes in mutual fund = â‚¹ 120000

Amount received by Mr. Fernandes after 2 years = â‚¹ 192000

âˆ´ Profit earned by Mr. Fernandes

= Amount received â€“ Amount invested

= 192000- 120000

= â‚¹72000

âˆ´ Mr. Fernandes percentage of profit Profit earned

= 60%

From (i) and (ii),

Investment of Mr. Fernandes turned out to be more profitable.

**Question 5.Sameera spent 90% of her income and donated 3% for socially useful causes. If she was left with â‚¹ 1750 at the end of the month, what was her actual income ?Solution:**

Let the actual income of Sameera be â‚¹ x.

Sameera spent 90% of her income and donated 3%.

âˆ´ Sameeraâ€™s total expenditure

= (3% + 90%) of x

= 93% of x

= 0.93x

Now, Savings = Income â€“ Expenditure

âˆ´ 1750 = x-0.93x

âˆ´ 1750 = 0.07x

âˆ´ The actual income of Sameera is â‚¹ 25000.

**Intext Questions and Activities**

**Question 1.Amita invested some part of â‚¹ 35000 at 4% and the rest at 5% interest for one year. Altogether her gain was â‚¹ 1530. Find out the amounts she had invested at the two different rates. Write your answer in words. (Textbook pg. no. 97)Solution:**

Let the amount invested at the rate of 4% and 5% be â‚¹ x and â‚¹ y respectively.

According to the first condition, total amount invested = â‚¹ 35000

âˆ´ x + y = 35000 â€¦(i)

According to the second condition,

total interest received at 4% and 5% is â‚¹ 1530.

âˆ´ 4 % of x + 5 % of y = 1530

âˆ´ 4x + 5y = 153000 â€¦(ii)

Multiplying equation (i) by 4, we get

4x + 4y = 140000 â€¦(iii)

Subtracting equation (iii) from (ii),

Substituting y = 13000 in equation (i),

x + 13000 = 35000

âˆ´ x = 35000 â€“ 13000 = 22000

âˆ´ Amita invested â‚¹ 22000 at the rate of 4% and â‚¹ 13000 at the rate of 5%.