Answers:

i) A. ₹ 1,50,000

ii) B. 2018-19

Solution:

Let Mr. Shekhar’s income be ₹ x.
He spends 60% of his income.
So, the remaining income
= 100% − 60%
= 40%

∴ The remaining income

= \(\displaystyle \frac{40}{100} \times x\)

= \(\displaystyle \frac{2x}{5}\)

From the remaining income, he donates ₹ 300 to an orphanage.
∴ Amount remaining after donation

= \(\displaystyle \frac{2x}{5}\) − 300

According to the given information, the amount left is ₹ 3,200

∴ \(\displaystyle \frac{2x}{5} - 300 = 3200\)

∴ \(\displaystyle \frac{2x}{5} = 3200 + 300\)

∴ \(\displaystyle \frac{2x}{5} = 3500\)

∴ \(\displaystyle x = \displaystyle \frac{3500 \times 5}{2}\)

∴ \(\displaystyle x = 8750\)

Thus, Mr. Shekhar's income is ₹ 8,750.

Solution:

Let’s calculate Hiralal’s percentage profit in 2 years:
Principal = ₹ 2,15,000
Amount = ₹ 3,05,000

Profit = Amount − Principal
∴ Profit = 305000 − 215000
∴ Profit = ₹ 90,000

Now, Percentage profit

= \(\displaystyle \frac{Profit}{Investment} \times 100\)

= \(\displaystyle \frac{90000}{215000} \times 100\)

= \(\displaystyle \frac{9}{215} \times 100\)

= \(\displaystyle \frac{1800}{43}\)

\(\displaystyle \approx 41.86 %\)

Now, let’s calculate Ramniklal’s percentage profit in 2 years:

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

P = Principal amount = ₹ 1,40,000
r = Rate of interest = 8%
n = Time period = 2 years
A = Amount = ?

Now, using the formula for compound interest:

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

Substituting the values in the formula, we get:

\(A = 140000 \left(1 + \displaystyle \frac{8}{100}\right)^2\)

∴ \(A = 140000 \displaystyle \left(1.08\right)^2\)

∴ \(A = 140000 \times 1.1664\)

∴ \(A = 163296\)

A = ₹ 1,63,296

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

I = A − P
∴ I = 163296 − 140000
∴ I = ₹ 23,296

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

Percentage return = \(\displaystyle \frac{Interest}{Principal} \times 100\)

∴ Percentage return = \(\displaystyle \frac{23296}{140000} \times 100\)

∴ Percentage return = 16.64% ... (ii)

From (i) and (ii), we see that Mr. Ramniklal’s investment was more profitable as compared to Mr. Hiralal’s investment.

Solution:

Principal = ₹ 24,000 + ₹ 56,000 = ₹ 80,000
Rate of interest = 7.5%
n = Time period = 3 years
A = Amount = ?

∴ Amount after compound interest:

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

Substituting the values in the formula, we get:

\(A = 80000 \left(1 + \displaystyle \frac{7.5}{100}\right)^3\)

∴ \(A = 80000 \displaystyle \left(1.075\right)^3\)

∴ \(A = 80000 \times 1.2422\)

∴ \(A = 99376\)

∴ A = ₹ 99,376

Solution:

Let Mr. Manohar's income be x.

He gave 20% of his income to his elder son and 30% of his income to his younger son.

∴ The amount given to his sons
= 20% of x + 30% of x
= 50% of x

∴ The amount remaining
= 100% − 50%
= 50% of x

= \(\displaystyle \frac{50}{100} \times x\)

= ₹ \(\displaystyle \frac{x}{2}\)

Out of this balance, he donates 10% to a school.
∴ The amount donated to the school

= 10% of \(\displaystyle \frac{x}{2}\)

= \(\displaystyle \frac{10}{100} \times \frac{x}{2}\)

= \(\displaystyle \frac{x}{20}\)

Therefore, the remaining amount with Mr. Manohar

= \(\displaystyle \frac{x}{2} - \frac{x}{20}\)

= \(\displaystyle \frac{10x - x}{20}\)

= ₹ \(\displaystyle \frac{9x}{20}\)

But, this balance is given as ₹ 1,80,000

∴ \(\displaystyle \frac{9x}{20}\) = 1,80,000

∴ x = \(\displaystyle \frac{180000 \times 20}{9}\)

∴ x = 400000

Therefore, Mr. Manohar’s income is ₹ 4,00,000.

Solution:

Let, the initial income of Kailash be ₹ x.

He used to spend 85% of x
= \(\displaystyle \frac{85}{100} \times x\)

= 0.85x

Now, his income increased by 36%.

∴ New income = x + 36% of x = \(\displaystyle x + \frac{36}{100} \times x\)

= 1.36x ... (i)

But, his expenses also increased by 40% of his earlier expenses.

New expenses
= Earlier expenses + 40% of earlier expenses

= 0.85x + 40% of 0.85x

= 0.85x + \(\displaystyle \frac{40}{100} \times 0.85x\)

= 0.85x + \(\displaystyle \frac{34x}{100}\)

= 0.85x + 0.34x
= 1.19x ... (ii)

Now,
New savings = New income − New expenses

= 1.36x − 1.19x
= ₹0.17x ... [From (i) and (ii)]

And percentage savings

= \(\displaystyle \frac{Savings}{Earnings} \times 100\)

= \(\displaystyle \frac{0.17x}{1.36x} \times 100\)

= \(\displaystyle \frac{17}{136} \times 100\)

= \(\displaystyle \frac{1700}{136}\)

= 12.5 %

∴ Kailash now saves 12.5 % of his earnings.

Solution:

Let, the total incomes of Ramesh, Suresh and Preeti be ₹ x, ₹ y and ₹ z respectively.

According to the given information,

x + y + z = 807000 ... (i)

The percentages of their expenses are 75%, 80% and 90% respectively.

∴ Ramesh’s expenses = 75% of x = \(\displaystyle \frac{75}{100} \times x\)

∴ Ramesh’s savings = x − \(\displaystyle \frac{75}{100} \times x\)

∴ Ramesh’s savings = \(\displaystyle \frac{25x}{100}\) = \(\displaystyle \frac{x}{4}\) ... (ii)

Suresh’s expenses = 80% of y = \(\displaystyle \frac{80}{100} \times y\)

∴ Suresh’s savings = y − \(\displaystyle \frac{80}{100} \times y\)

∴ Suresh’s savings = \(\displaystyle \frac{20y}{100}\) = \(\displaystyle \frac{y}{5}\) ... (iii)

Preeti’s expenses = 90% of z = \(\displaystyle \frac{90}{100} \times z\)

∴ Preeti’s savings = z − \(\displaystyle \frac{90}{100} \times z\)

∴ Preeti’s savings = \(\displaystyle \frac{10z}{100}\) = \(\displaystyle \frac{z}{10}\) ... (iv)

Now, their savings are in the ratio 16 : 17 : 12 ... (Given)

Let the common multiple of these ratios be m.

Their savings are 16m, 17m and 12m respectively. ... (v)

From (ii) and (v),

\(\displaystyle \frac{x}{4} = 16m\)

∴ x = 16m × 4
∴ x = 64m ... (vi)

From (iii) and (v),

\(\displaystyle \frac{y}{5} = 17m\)

∴ y = 17m × 5
∴ y = 85m ... (vii)

From (iv) and (v),

\(\displaystyle \frac{z}{10} = 12m\)

∴ z = 12m × 10
∴ z = 120m ... (viii)

Now, x + y + z = 807000 ... [From (i)]

∴ 64m + 85m + 120m = 807000

∴ 269m = 807000

∴ m = \(\displaystyle \frac{807000}{269}\) = 3000 ... (ix)

∴ Ramesh’s savings
= 16m = 16 × 3000 = ₹ 48,000

∴ Suresh’s savings
= 17m = 17 × 3000 = ₹ 51,000

∴ Preeti’s savings
= 12m = 12 × 3000 = ₹ 36,000

Solution:

1. Mr. Kadam is 35 years old.
   ∴ We refer to Table I:

   Mr. Kadam’s income is more than ₹ 10,00,000.

   ∴ Income Tax
   = 112500 + 30 % of (1335000 - 1000000)
   = 112500 + 30 % of 335000
   = 112500 + 100500
   = ₹ 2,13,000

   = \(\displaystyle 112500 + \frac{30}{100} \times 335000\)

   = \(\displaystyle 112500 + 100500\)

   = ₹ 2,13,000 ... (i)

   Education Cess (2%):
   = 2% of ₹ 2,13,000

   = \(\displaystyle \frac{2}{100} \times 213000\)

   = ₹ 4,260 ...  ... (ii)

   Higher Education Cess (1%):
   = 1% of ₹ 2,13,000

   = \(\displaystyle \frac{1}{100} \times 213000\)

   = ₹ 2,130 ...  ... (iii)

   ∴ Total income tax payable = 213000 + 4260 + 2130
   = 219390 ... (iv)

   ∴ Total income tax payable by Mr. Kadam is ₹ 2,19,390



2. Mr. Khan is 65 years old.
   ∴ We refer to Table II:

   Mr. Khan’s income is ₹ 4,50,000.

   ∴ Income Tax
   = 5 % of (450000 - 300000)
   = 5 % of 150000

   = \(\displaystyle \frac{5}{100} \times 150000\)

   = \(\displaystyle 7500\)

   = ₹ 7,500 ... (i)

   Education Cess (2%):
   = 2% of ₹ 7,500

   = \(\displaystyle \frac{2}{100} \times 7500\)

   = ₹ 150 ...  ... (ii)

   Higher Education Cess (1%):
   = 1% of ₹ 7,500

   = \(\displaystyle \frac{1}{100} \times 7500\)

   = ₹ 75 ...  ... (iii)

   ∴ Total income tax payable = 7500 + 150 + 75
   = 7725 ... (iv)

   ∴ Total income tax payable by Mr. Khan is ₹ 7,725



3. Miss Varsha is 26 years old.
   ∴ We refer to Table I:

   Miss Varsha’s income is ₹ 2,30,000.

   ∴ Income Tax
   = Nil (As her income is below ₹ 2,50,000)

   ∴ Total income tax payable by Miss Varsha is ₹ 0