Solution:

Suppose, Alka gets ₹ x every month.

Now, she spends 90% of the money.

∴ She saves
100% − 90% = 10% of the money.

∴ She saves \(\displaystyle \frac{10}{100} \times x\) = ₹ \(\displaystyle \frac{x}{10}\) ... (i)

But, she saves ₹ 120 ... (Given) ... (ii)

∴ \(\displaystyle \frac{x}{10} = 120\) ... from (i) and (ii)

∴ x = 120 × 10

∴ x = = ₹ 1200

∴ Alka gets ₹ 1,200 every month.

Solution:

Sumit borrowed a capital of ₹ 50000 to start his food products business.

In the first year he suffered a loss of 20%.

Let's calculate Sumit’s loss on ₹ 50000

Loss = \(\displaystyle \frac{20}{100} \times 50000\)

∴ Loss = ₹ 10000.

∴ The remaining capital after the loss
= 50000 − 10000
= ₹ 40000.

He invested this remaining capital in a new sweet mart business and made a profit of 5%.

Let's calculate Sumit’s profit on ₹ 40000

Profit = \(\displaystyle \frac{5}{100} \times 40000\)

∴ Profit = ₹ 2000.

Now, the amount of capital remaining after this profit
= 40000 + 2000
= ₹ 42000.

Here, the remaining capital is less than the original capital.

∴ Sumit suffered a loss.

Now,
Loss = Original Capital − Remaining Capital

∴ Loss = 50000 − 42000

∴ Loss = ₹ 8000

Now, let’s calculate Sumit’s percentage loss.

Percentage loss = \(\displaystyle \frac{8000}{50000} \times 100\)

∴ Percentage loss = 16%

Hence, Sumit suffered a loss of 16% on his original capital.

Solution:

Let Nikhil’s monthly income be ₹ x.

Nikhil spent 5% of his income on his children’s education, invested 14% in shares, deposited 3% in a bank and used 40% for his daily expenses.

Thus, the total expenditure
= 5% + 14% + 3% + 40%
= 62% of income.

Therefore, the money left with him
= 100% − 62%
= 38% of income.

According to the given information,

38% of x = 19000

∴ \(\displaystyle \frac{38}{100} \times x\) = 19000

∴ x = \(\displaystyle \frac{19000 \times 100}{38} \)

∴ x = 50000

Thus, Nikhil's income that month was ₹ 50,000.

Solution:

For Mr. Sayyad:

Let's calculate the amount received after 2 years with compound interest.

P = Principal amount = 40000

r = Rate of interest = 8%

n = Time period = 2 years

A = Amount = ?

Now,

\(A = P \left(1+\frac{r}{100}\right)^n\)

Substituting the values in the formula, we get:

\(A = 40000 \left(1 + \displaystyle \frac{8}{100}\right)^2\)

∴ \(A = 40000 \displaystyle \left(1.08\right)^2\)

∴ \(A = 40000 \times 1.1664\)

∴ \(A = 46656\)

A = ₹ 46,656

Now, let's calculate the interest earned by Mr. Sayyad.

I = A − P

∴ I = 46656 − 40000

∴ I = ₹ 6,656

Now, let's calculate the percentage return on Mr. Sayyad’s investment.

Percentage return = \(\displaystyle \frac{I}{P} \times 100\)

∴ Percentage return = \(\displaystyle \frac{6656}{40000} \times 100\)

∴ Percentage return = 16.64% ... (i)

For Mr. Fernandes:

Investment = ₹ 1,20,000

Amount received after 2 years = ₹ 1,92,000

Now, let's calculate the interest earned by Mr. Fernandes.

I = A − P

∴ I = 192000 − 120000

∴ I = ₹ 72,000

Now, let's calculate the percentage return on Mr. Fernandes' investment.

Percentage return = \(\displaystyle \frac{I}{P} \times 100\)

∴ Percentage return = \(\displaystyle \frac{72000}{120000} \times 100\)

∴ Percentage return = 60% ... (ii)

Comparing (i) and (ii), we see that Mr. Fernandes' investment turned out to be more profitable.

Solution:

Let Sameera’s income be ₹ x.

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

Thus, the total expenditure
= 90% + 3%
= 93% of income.

Therefore, the money left with her
= 100% − 93%
= 7% of income (x).

According to the given information,

7% of x = 1750

∴ \(\displaystyle \frac{7}{100} \times x\) = 1750

∴ x = \(\displaystyle \frac{1750 \times 100}{7} \)

∴ x = 25000

Thus, Sameera’s actual income is ₹ 25,000.