Let her monthly income be Rs 'x'

Savings = Rs 120

Expenditure = 90% of x = \(\frac{90}{100}x\)

Income = Expenditure + Savings

x = \(\frac{90}{100}x\) + 120

x - 120 = \(\frac{90}{100}x\)

100 (x - 120) = 90x

100x - 12000 = 90x

100x - 90x = 12000

10x = 12000

∴ x = \(\frac{12000}{10}\) = 1200

Thus, total monthly salary = Rs 1200.

Sumit borrowed capital = Rs. 50000

Loss incurred in the first year = 20% x 50000

\(\frac{20}{100}\) x 50000 = ₹ 10,000

Remaining Capital = Total Capital - Loss

50,000 - 10,000 = ₹ 40,000

Profit in food products business = 5% of ₹ 40,000

\(\frac{5}{100}\) x 40,000 = ₹ 2000

Capital held by Sumit after two years = 40,000 + 2000 = ₹ 42,000

Total loss in original capital = 50,000 - 42,000 = ₹ 8,000

Loss% = \(\frac{8000}{50000}\) x 100 =16%

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

Let Nikhil's monthly income be ₹ x.

Nikhil's expenses :

(i) Children's education : 5%

(ii) Investment in shares : 14%

(iii) Deposited in a bank : 3%

(iv) Daily expenses : 40%

∴ total expenses = (5 + 14 + 3 + 40)% = 62% of monthly income.

∴ total monthly expenses = ₹ \(\frac{62x}{100}\)

Balance = income - expenditure

∴ 19000 = x - \(\frac{62x}{100}\) = \(\frac{100x-62x}{100}\)

∴ 19000 x 100 = 100x – 62x          ... (Multiplying both the sides by 100)

∴ 19000 × 100 = 38x

∴ x = \(\frac{19000×100}{38}\) = 50000

∴ Nikhil's monthly income is ₹ 50,000.

Amount deposited by Mr. Sayyed = Rs 40,000

Rate of interest = 8%

Time = 2 years

CI = Amount - Principle

= P\((1+\frac{R}{100})^n\)  - P

= 40000\((1+\frac{8}{100})^2\)  - 40000  

= 40000\((\frac{100+8}{100})^2\)  - 40000

= 40000(1.08)² - 40000

= 40000 (1.1664 - 1)

= 40000 × 0.1664

= Rs. 6656

Percentage profit = \(\frac{6656}{40000}\) × 100 = 16.64%

Investment in mutual funds by Mr. Fernandes = Rs 1, 20, 000

The amount Mr. Fernandes got at the end of 2 years from the mutual fund = Rs 1,92,000

Profit =1,92,000 - 1,20,000 = Rs. 72000

Percentage profit from mutual funds = \(\frac{72000}{120000}\) × 100 = 60%

Thus, investment by Mr. Fernandes turned out to be more profitable.

Let Sameera's monthly income be ₹ x.

She spent 90% of her income.

Donated 3%.

∴ she spent (90 + 3)% = 93% of her income.

i.e. she spent ₹ \(\frac{93x}{100}\)

Savings = income – expenditure

1750 = x - \(\frac{93x}{100}\) = \(\frac{100x-93x}{100}\)

∴ 1750 × 100 = 100x - 93x   ... (Multiplying both the sides by 100)

∴ 7x = 1750 × 100

∴ x = 175000/7 = 25000

∴ Sameera's monthly income is ₹ 25,000.

(i) Miss Nikita is age 27, and her taxable income is Rs 2,34,000. She doesn't need to pay income tax as her earnings are less than Rs 2,50,000.

(ii) Mr. Kulkarni is of age 36 years and his taxable income is Rs 3,27,000. So, his taxable income falls in the slab of 2,50,001 to 5,00,000. Thus, he needs to pay the income tax.

(iii) Miss Mehta is of age 44 and has a taxable income of Rs 5,82,000. She needs to pay the income tax as her taxable income falls in the slab of Rs 5,00,001 to 10,00,000.

(iv) Mr. Bajaj is of age 64 years and has a taxable income of Rs 8,40,000. He needs to pay the income tax as his taxable income falls in the slab of Rs 5,00,001 to 10,00,000.

(v) Mr. Desilva is of age 81 years and has a taxable income of Rs 4,50,000. He doesn't need to pay income tax as he is in the super senior category and has a taxable income of less than Rs 5,00,000.

Monthly Income = Rs. 42,000

Gross annual income = Rs. 42,000 x 12 = Rs. 5,04,000

Applicable deductions:

Monthly GPF contribution = Rs. 3000

Annual GPF contribution = Rs. 3000 x 12 = Rs. 36,000

NSC = Rs. 15,000

Donation in PM's relief fund = Rs. 12000

Total applicable deductions = Rs. 36,000 + 15,000 + 12,000 = Rs. 63,000

Total taxable income = Gross annual income - total applicable deductions

= Rs. 5,04,000 - Rs. 63,000 = Rs. 4,41,000

Now the Total taxable income falls in the slab of 2,50,001 to 5,00,000.

So, Income tax = 5% of (Taxable income - 2,50,000)

= 5% of (441000 - 250000)

= \(\frac{5}{100}\) x 191000 = =₹ 9550

Education Cess = 2% of Income Tax

= 9550 x \(\frac{2}{100}\)

= Rs. 191

Secondary and Higher Education Cess = 1% of Income Tax

= 9550 x \(\frac{1}{100}\)

= Rs. 95.5

Total tax to be paid = Income tax + education cess + secondary and higher education cess

= 9550 + 191 + 95.5 = Rs. 9836.5

∴ Mr. Kartar Singh will have to pay 9836.50 income tax.

(A) 1,50,000 rupees

[As per savings under section 80C : ₹ 1,50,000]

(B) 2018-19

[Assessment year is the one following financial year.]

Let Mr. Shekhar's income be Rs x.

Money spent = 60% of x = \(\frac{60x}{100}\)

Money donated in orphanage = Rs 300

Money left = Rs 3200

Money spent + Money donated + Money left = Total income

\(\frac{60x}{100}\) + 300 + 3200 = x 

\(\frac{6x}{10}\) + 3500 = x

x - \(\frac{6x}{10}\) = 3500

\(\frac{10x-6x}{10}\) = 3500

\(\frac{4x}{10}\) = 3500

4x = 35000

x = 35000/4 = 8750

Thus, Mr. Shekhar's income is Rs 8750.

Mr. Hiralal's investment = Rs. 2,15,000

Return of investment = Rs. 3,05,000

Profit = Mr. Hiralal's investment - Return of investment

= 3,05,000 - 2,15,000 = Rs. 90,000

Profit % = \(\frac{90000}{215000}\) x 100 = 41.86%

For Ramaniklal,

P = 140000, R = 8%, n = 2 years

Compound interest = I = P\([(1+\frac{R}{100})^n-1]\)

= 140000\([(1+\frac{8}{100})^2-1]\)

= 140000\([(\frac{108}{100})^2-1]\)

= 140000 [(1.08)² - 1]

= 140000(1.1664 - 1)

= 140000 × 0.1664

= 23296

Profit% = \(\frac{23296}{140000}\) x 100 = 16.64%

Thus, Mr. Hiralal's investment is more profitable.

Total investment = Rs 24,000 + Rs 56,000 = Rs 80,000

R = 7.5%, n = 3 years

Amount = P\((1+\frac{R}{100})^n\)

= 80,000 ×\((1+\frac{7.5}{100})^3\)

= 80,000 × \((1+\frac{75}{1000})^3\)

= 80,000 × \((1+\frac{3}{40})^3\)

= 80,000 × \((\frac{43}{40})^3\)

= \((\frac{80000×43×43×43}{40×40×40})^3\)

= 99383.75

Thus, the amount after 3 years will be Rs 99383.75.

Let Mr. Manohar's income be Rs x.

Money given to elder son = 20% of x = \(\frac{20x}{100}\)

Money given to younger son = 30% of x = \(\frac{30x}{100}\)

Balance = x - \((\frac{20x}{100}+\frac{30x}{100}\)

= x - \(\frac{50x}{100}\) = \(\frac{100x-50x}{100}\) = Rs \(\frac{50x}{100}\)

10% of the remaining income is donated to the school.

Donation = \(\frac{50x}{100}\) × \(\frac{10}{100}\) = Rs \(\frac{5x}{100}\)

Income - Expenditure = Savings

x - \((\frac{20x}{100}+\frac{30x}{100}+\frac{5x}{100}\) = 180000

x - \(\frac{55x}{100}\) = 180000

\(\frac{100x-55x}{100}\) = 180000

\(\frac{45x}{100}\) = 180000

∴ 45x = 180000 ×100

∴ x = 18000000/45 = 400000

 Thus, Mr. Manohar's income is Rs. 4,00,000.

Let Kailash's income be ₹ x.

He spends 85% of x = 0.85x.

His income increased by 36%

∴ new income is x + x(36%) = x + 0.36x = 1.36x.

His expenses increased by 40%

Previous expense was 0.85x

∴ new expense = 0.85x + 40% of 0.85x

= 0.85x + \(\frac{40}{100}\)×0.85x = 0.85x + 0.34x = 1.19x.

∴ saving = earning - expense = ₹(1.36x - 1.19x) = ₹ 0.17x

Percent saving = \(\frac{savings}{earnings}\) × 100 = \(\frac{0.17x}{1.36x}\) x 100 = 12.5%

 ∴ Kailash's savings is 12.5%

Let the annual incomes of Ramesh,

Suresh and Preeti be ₹ a, ₹ b and ₹ c respectively.

∴ a + b + c = 807000    …..(i)

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

∴ savings of Ramesh =a - 75% of a = a - \(\frac{75}{100}\) × a

= \(a-\frac{75a}{100}\) 

= \(\frac{100a-75a}{100}\)

= \(\frac{25a}{100}\)

= \(\frac{a}{4}\)…..(ii)

that of Suresh = b - 80% of b = b - \(\frac{80}{100}\) × b

= \(a-\frac{80b}{100}\) 

= \(\frac{100b-80b}{100}\)

= \(\frac{20b}{100}\)

= \(\frac{b}{5}\)        …..(iii)

and that of Preeti = c - 90% of c = c - \(\frac{90}{100}\) × c

= \(a-\frac{90c}{100}\) 

= \(\frac{100c-90c}{100}\)

= \(\frac{10c}{100}\)

= \(\frac{c}{10}\)     …..(iv)

Their savings are in the ratio 16 : 17 : 12.

Let the common multiple of these ratios be x.

Then their saving are ₹ 16x, ₹ 17x and ₹ 12x respectively

From (ii), (iii), (iv) and (v)

\(\frac{a}{4}\) = 16x, \(\frac{b}{5}\) = 17x, \(\frac{c}{10}\) = 12x

∴ a = 64x; b = 85x and c= 120x.

∴ a + b + c = 64x + 85x + 120x = 269x

∴ from (i), 269x = 807000

∴ x = \(\frac{807000}{269}\) = 3000

Annual saving of Ramesh = 16x = 16 x 3000 = ₹ 48000

that of Suresh = 17x = 17 x 3000 = ₹ 51000

and that of Preeti = 12x = 12 x 3000 = ₹ 36000

∴ The annual savings of Ramesh, Suresh and Preeti are ₹ 48,000, ₹ 51,000 and ₹ 36,000 respectively.

Taxable income = Rs. 13,35,000

Income tax = Rs. 1,12,500 + 30% (Rs. 13,35,000 - Rs. 10,00,000)

= Rs. 1,12,500 + \(\frac{30}{100}\) × 335000

= Rs. 1,12,500 + Rs. 1,00,500 = Rs. 2,13,000

Education Cess = 2% of income tax

= Rs. 2,13,000 x \(\frac{2}{100}\) = Rs. 4,260

And Secondary and Higher Secondary Education Cess = 1%

= Rs. 2, 13, 000 x \(\frac{1}{100}\) = Rs. 2,130

Total income tax = Rs. 2,13,000 + Rs. 4,260 + Rs. 2,130 = Rs. 2,19,390

Mr Kadam will have to pay ₹ 2,19,390 income tax.

Taxable income = Rs. 4,50,000

Income tax = 5% (Rs. 4,50,000 - Rs. 3,00,000) = \(\frac{5}{100}\) × 150,000 = Rs. 7500

Education cess = 2% of income tax = \(\frac{2}{100}\) × 7500 = Rs. 150

Secondary and Higher Education cess = 1% of income tax = \(\frac{1}{100}\) × 7500 = 75

Total income tax = Income tax + Education cess + Secondary and higher education cess

= 7500 + 150 + 75 = Rs. 7725

Mr Khan will have to pay ₹ 7725 income tax.

As per the table I, her income is less than ₹ 2,50,000.

∴ Miss Varsha will not have to pay income tax.