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

Let Alka’s monthly income be ₹ x.

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

∴ Amount spent by Alka = 90% of x

Now, Savings = Income – Expenditure

∴ 120 = x – 0.9x

∴120 = 0.1 x

∴ x = 1200

Alka gets ₹ 1200 monthly.

**Question 2.Sumit borrowed a capital of ₹ 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 = ₹ 50000

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

∴ Loss suffered in the first year = 20% of 50000

= ₹10000

Remaining capital = Original capital – loss suffered = 50000- 10000

= ₹ 40000

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

Profit in sweets business = 5% of 40000

= ₹ 2000

New capital with Sumit after the profit in new sweets business = 40000 + 2000 = ₹42000

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 – New capital

= 50000 – 42000 = ₹ 8000

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

Question 3.

Nikhil spent 5% of his monthly income on his children’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 ₹ 19,000. What was his income that month?

Solution:

Let the monthly income of Nikhil be ₹ x.

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

∴ Total investment = (14% + 3%) of x

= 17% of x

= 0.1 7 x

Nikhil spent 5% on his children’s education and used 40% for his daily expenses.

∴ Total expenditure = (5% + 40%) of x

= 45% of x

= 0.45x

Amount left with Nikhil = 19,000

Amount left with Nikhil = Income – (Total investment + Total expenditure)

∴ 19000 = x – (0.17x + 0.45x)

∴ 19000 = x – 0.62x ,

∴ 19000 = 0.38x

= 50000

∴ The monthly income of Nikhil is ₹ 50000.

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

Mr. Sayyad:

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

∴ Compound interest (I)

= Amount (A) – Principal (P)

= 40000 [(1 +0.08)

^{2}– 1]

= 40000 [(1.08)

^{2}– 1]

= 40000(1.1664 – 1)

= 40000 (0.1664)

= ₹ 6656

∴ Mr. Sayyad’s percentage of profit Interest

Mr. Fernandes:

Amount invested by Mr. Fernandes in mutual fund = ₹ 120000

Amount received by Mr. Fernandes after 2 years = ₹ 192000

∴ Profit earned by Mr. Fernandes

= Amount received – Amount invested

= 192000- 120000

= ₹72000

∴ 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 ₹ 1750 at the end of the month, what was her actual income ?Solution:**

Let the actual income of Sameera be ₹ x.

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

∴ Sameera’s total expenditure

= (3% + 90%) of x

= 93% of x

= 0.93x

Now, Savings = Income – Expenditure

∴ 1750 = x-0.93x

∴ 1750 = 0.07x

∴ The actual income of Sameera is ₹ 25000.

**Intext Questions and Activities**

**Question 1.Amita invested some part of ₹ 35000 at 4% and the rest at 5% interest for one year. Altogether her gain was ₹ 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 ₹ x and ₹ y respectively.

According to the first condition, total amount invested = ₹ 35000

∴ x + y = 35000 …(i)

According to the second condition,

total interest received at 4% and 5% is ₹ 1530.

∴ 4 % of x + 5 % of y = 1530

∴ 4x + 5y = 153000 …(ii)

Multiplying equation (i) by 4, we get

4x + 4y = 140000 …(iii)

Subtracting equation (iii) from (ii),

Substituting y = 13000 in equation (i),

x + 13000 = 35000

∴ x = 35000 – 13000 = 22000

∴ Amita invested ₹ 22000 at the rate of 4% and ₹ 13000 at the rate of 5%.