Mathematics Part i Solutions Solutions for Class 9 Math Chapter 6 - Financial Planning

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Page No 98:

Question 1:

Alka spends 90% of the money that she receives every month, and saves Rs. 120. How much money does she get monthly ?

Answer:

Let her monthly income be Rs x.
Savings = Rs 120
Expenditure = $90 % of x = \frac{90}{100} x = \frac{9 x}{10}$
Savings = Total monthly salary $-$ Expenditure = $x - \frac{9 x}{10} = \frac{x}{10}$ = 120
$x = 10 \times 120 = 1200$
Thus, total monthly salary = Rs 1200

Page No 98:

Question 2:

Sumit borrowed a capital of Rs. 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 ?

Answer:

Sum borrowed = Rs 50,000
Loss = 20% of Rs 50, 000 = $\frac{20}{100} \times 50, 000 = 10, 000$
Remaining sum = Rs 50,000 $-$ Rs 10,000 = Rs 40,000
Profit = 5% of Rs 40,000 = $\frac{5}{100} \times 40, 000 = Rs 2000$
Capital after profit = Rs 40,000 + Rs 2000 = Rs 42,000
Overall Loss = $Rs 50, 000 - Rs 42, 000 = Rs 8000$
Loss% = $\frac{8000}{50000} \times 100 = 16 %$

Page No 98:

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 Rs. 19,000. What was his income that month ?.

Answer:

Let the monthly income be Rs x.
Money spent on children's education = 5% of x = $\frac{5}{100} x$
Money spent on shares = 14% of x = $\frac{14}{100} x$
Money deposited in banks = 3% of x = $\frac{3}{100} x$
Money spent on daily expenses = 40% of x = $\frac{40}{100} x$
Savings = Rs 19,000
$\frac{5}{100} x$ + $\frac{14}{100} x$ + $\frac{3}{100} x$ + $\frac{40}{100} x$ + 19000 = x
$\Rightarrow \frac{62}{100} x + 19000 = x \Rightarrow x - \frac{62}{100} x = 19000 \Rightarrow \frac{38}{100} x = 19000 \Rightarrow x = 50, 000$
Thus, monthly income = Rs 50,000

Page No 98:

Question 4:

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

Answer:

Amount deposited by Mr. Sayyed = Rs 40,000
Rate of interest = 8%
Time = 2 years
CI = Amount $-$ Principle
$= P {(1 + \frac{R}{100})}^{n} - P = 40, 000 {(1 + \frac{8}{100})}^{2} - 40, 000 = 40, 000 [{(\frac{108}{100})}^{2} - 1] = 40, 000 (1.1664 - 1) = 40, 000 \times 0.1664 = Rs 6656$
$Percentage profit = \frac{6656}{40, 000} \times 100 = 16.64 %$
Investment in mutual funds by Mr. Fernandes =Rs 1,20,000
Return of investment = Rs 1,92,000
Profit = $1, 92, 000 - 1, 20, 000 = Rs 72, 000$
Percentage profit from mutual funds = $\frac{72, 000}{1, 20, 000} \times 100 = 60 %$
Thus, investment by Mr. Fernandes turned out to be more profitable.

Page No 98:

Question 5:

Sameera spent 90% of her income and donated 3% for socially useful causes. If she left with Rs. 1750 at the end of the month, what was her actual income ?

Answer:

Let Sameera's actual income be Rs x.
Money spent = 90% of x = $\frac{90}{100} x$
Money donated = 3% of x = $\frac{3}{100} x$
Money left = Rs 1750
Money spent + money donated + money left = Total income
$\Rightarrow \frac{90}{100} x + \frac{3}{100} x + 1750 = x \Rightarrow 7 x = 175000 \Rightarrow x = 25000$
Thus, Sameera's actual income is Rs 25000

Page No 106:

Question 1:

Observe the table given below. Check and decide, whether the individuals have to pay income tax.

S. No.	Individuals	Age	Taxable Income (rs )	Will have to pay income tax or not
(i) (ii) (iii) (iv) (v)	Miss Nikita Mr.Kulkarni Miss Mehta Mr. Bajaj Mr. Desilva	27 36 44 64 81	rs 2,34,000 rs 3,27,000 rs 5,82,000 rs 8,40,000 rs 4,50,000

Answer:

(i) Miss Nikita is of age 27 and her taxable income is Rs 2,34,000.
She doesnt need to pay income tax as her earning is 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 taxable income of Rs 4,50,000.
He doesnt need to pay income tax as he is in the super senior category and has taxable income of less than Rs 5,00,000.

Page No 106:

Question 2:

Mr. Kartarsingh (age 48 years) works in a private company. His monthly income after deduction of allowances is Rs. 42,000 and every month he contributes Rs. 3000 to GPF. He has also bought Rs. 15,000 worth of NSC (National Savings Certificate) and donated Rs. 12,000 to the PM's Relief Fund. Compute his income tax.

Answer:

Monthly Income = Rs 42,000
Gross annual income = Rs 42,000 $\times$ 12 = Rs 5,04,000
Applicable deductions:
Monthly GPF contribution = Rs 3000
Annual GPF contribution = Rs 3000 $\times$ 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 = (Taxable income $-$ 2,50,000) $\times \frac{5}{100}$ = Rs 9550
Education cess = $9550 \times \frac{2}{100} = Rs 191$
Secondary and higher education cess = $9550 \times \frac{1}{100} = Rs 95.5$
Total tax to be paid = Income tax + education cess + secondary and higher education cess = 9550 + 191 + 95.5
= Rs 9836.5

Page No 107:

Question 1:

Write the correct alternative answer for each of the following quesitons.

(i) For different types of investments what is the maximum permissible amount under section 80C of income tax ?

(A) 1,50,000 rupees (B) 2,50,000 rupees (C) 1,00,000 rupees (D) 2,00,000rupees

(ii) A person has earned his income during the financial year 2017-18. Then his assessment year is ....

Answer:

(i) Under section 80 C of income tax, the maximum permissible amount is Rs 1,50,000.
Hence, the correct answer is option A.

(ii) The assessment year for the person who earned his income during 2017-18 will be 2018-19.
Hence, the correct answer is option B.

Page No 107:

Question 2:

Mr. Shekhar spends 60% of his income. From the balance he donates Rs. 300 to an orphanage. He is then left with Rs. 3,200. What is his income ?

Answer:

Let Mr. Shekhar's income be Rs x.
Money spent = 60% of x = $\frac{60}{100} x$
Money donated in orphanage = Rs 300
Money left = Rs 3200
Money spent + Money donated + Money left = Total income
$\Rightarrow \frac{60 x}{100} + 300 + 3200 = x \Rightarrow \frac{6 x}{10} + 3500 = x \Rightarrow x - \frac{6 x}{10} = 3500 \Rightarrow \frac{4 x}{10} = 3500 \Rightarrow x = 8750$
Thus, Mr. Shekhar's income is Rs 8750

Page No 107:

Question 3:

Mr. Hiralal invested Rs. 2,15,000 in a Mutual Fund. He got Rs. 3,05,000 after 2 years. Mr. Ramniklal invested Rs. 1,40,000 at 8% compound interest for 2 years in a bank. Find out the percent gain of each of them. Whose investment was more profitable ?

Answer:

Mr. Hiralal's investment = Rs 2,15,000
Return of investment = Rs 3,05,000
Profit = 3,05,000 $-$ 2,15,000 = Rs 90,000
Profit% = $\frac{90, 000}{2, 15, 000} \times 100 = 41.86 %$
Mr. Ramniklal invested Rs 1,40,000
Rate of interest = 8%
Time= 2 years
CI = A $-$ P
$= 1, 40, 000 {(1 + \frac{8}{100})}^{2} - 1, 40, 000 = 1, 40, 000 [{(\frac{108}{100})}^{2} - 1] = 1, 40, 000 \times 0.1664 = 23, 296$
Profit% = $\frac{23296}{140000} \times 100 = 16.64 %$
Thus, Mr. Hiralal's investment is more profitable.

Page No 107:

Question 4:

At the start of a year there were Rs. 24,000 in a savings account. After adding Rs. 56,000 to this the entire amount was invested in the bank at 7.5% compound interest. What will be the total amount after 3 years ?

Answer:

Total investment = Rs 24,000 + Rs 56,000 = Rs 80,000
Rate of interest = 7.5%
Time = 3 years
Amount = $P {(1 + \frac{R}{100})}^{n}$
$= 80, 000 {(1 + \frac{7.5}{100})}^{3} = 80, 000 {(\frac{107.5}{100})}^{3} = 80, 000 \times 1.242 = 99383.75$
Thus, the amount after 3 years will be Rs 99383.75.

Page No 107:

Question 5:

Mr. Manohar gave 20% part of his income to his elder son and 30% part to his younger son. He gave 10% of the balance as donation to a school. He still had Rs. 1,80,000 for himself. What was Mr. Manohar's income ?

Answer:

Let Mr. Manohar's income be Rs x.
Money given to elder son = 20% of x = $\frac{20}{100} x$
Money given to younger son = 30% of x = $\frac{30}{100} x$
Balance = $x - \frac{20 x}{100} - \frac{30 x}{100} = \frac{50}{100} x$
Donation = 10% of balance = $\frac{10}{100} (\frac{50}{100} x) = \frac{5 x}{100}$
Money left = Rs 1,80,000
Total income = Money to elder son + money to younger son + donation + money left
$\frac{30}{100} x + \frac{20}{100} x + \frac{5}{100} x + 1, 80, 000 = x \Rightarrow \frac{55}{100} x + 1, 80, 000 = x \Rightarrow x - \frac{55}{100} x = 1, 80, 000 \Rightarrow \frac{45}{100} x = 1, 80, 000 \Rightarrow x = 4, 00, 000$
Thus, Mr. Manohar's income is Rs 4,00,000.

Page No 107:

Question 6:

Kailash used to spend 85% of his income. When his income increased by 36% his expenses also increased by 40% of his earlier expenses. How much percentage of his earning he saves now ?

Answer:

Let the income be Rs 100.
Expenditure = 85% of Rs 100 = $\frac{85}{100} \times 100 = Rs 85$
New salary is 36% more than previous salary
So, new salary = 100 + $\frac{36}{100} \times 100$ = Rs 136
New expenditure increased by 40% of earlier expense.
New expenditure = $(100 + \frac{40}{100} \times 100) \times 85 = Rs 119$
Amount he saves now = New salary $-$ new expenditure
= Rs 136 $-$ Rs 119 = Rs 17
% saving = $\frac{17}{136} \times 100 = 12.5 %$

Page No 107:

Question 7:

Total income of Ramesh, Suresh and Preeti is 8,07,000 rupees. The percentages of their expenses are 75%, 80% and 90% respectively. If the ratio of their savings is 16 : 17 : 12, then find the annual saving of each of them.

Answer:

Let the savings of Ramesh, Suresh and Preeti be 16x, 17x and 12x.
Expenditure of Ramesh = 75% of income
So, Savings of Ramesh = 25% of income
We know
Saving = Income $-$ expenditure
16x = 25% of income
$\Rightarrow 16 x = \frac{25}{100} (income of Ramesh) \Rightarrow 64 x = income of Ramesh$
Similarly, Savings of Suresh = 20% of his income
So,
$17 x = 20 % (income of Suresh) \Rightarrow 17 x = \frac{20}{100} (income of Suresh) \Rightarrow 85 x = (income of Suresh)$
Savings of Preeti = 10% of her income
$\Rightarrow 12 x = \frac{10}{100} (income of Preeti) \Rightarrow 120 x = (income of Preeti)$
Given that total income of Ramesh, Suresh and Preeti is 8,07,000.
$64 x + 85 x + 120 x = 8, 07, 000 \Rightarrow 269 x = 8, 07, 000 \Rightarrow x = Rs 3000$
Savings of Ramesh = Rs 16 $\times 3000 = Rs 48000$
Savings of Suresh = Rs 85 $\times 3000 = Rs 51000$
Savings of Preeti = Rs 120 $\times 3000 = Rs 36000$

Page No 107:

Question 8:

Compute the income tax payable by following individuals.

(i) Mr. Kadam who is 35 years old and has a taxable income of Rs. 13,35,000.

(ii) Mr. Khan is 65 years of age and his taxable income is Rs. 4,50,000.

(iii) Miss Varsha (Age 26 years) has a taxable income of Rs. 2,30,000.

Answer:

(i) 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 + $\frac{30}{100} \times 3, 35, 000$
= Rs 1,12,500 + Rs 1,00,500
= Rs 2,13,000

(ii) Taxable income = Rs 4,50,000
Income tax = 5%(Rs 4,50,000 $-$ Rs 3,00,000)
$= \frac{5}{100} (1, 50, 000) = Rs 7500$

(iii) Taxable income = Rs 2,30,000
The tax payable is 0 as the taxable income is less than Rs 2,50,000.

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