Maharashtra Board Class 9 Maths Chapter 6 Set 6 Algebra Standard Part 1 Financial Planning Solutions

Question 1. Write the correct alternative answer for each of the following questions.
 

(i) For different types of investments what is the maximum permissible amount under section 80C of income tax ?
(A) Rs. 1,50,000
(B) Rs. 2,50,000
(C) Rs. 1,00,000
(D) Rs. 2,00,000
Answer: (A) Rs. 1,50,000
In simple words: Section 80C of the income tax act allows a maximum deduction of Rs. 1,50,000 for various investments and expenses. This helps reduce taxable income.

🎯 Exam Tip: Remember the maximum deduction limit under Section 80C, as this is a common factual question in financial planning.

Question.
(ii) A person has earned his income during the financial year 2017-18. Then his assessment year is....
(A) 2016-17
(B) 2018-19
(C) 2017-18
(D) 2015-16
Answer: (B) 2018-19
In simple words: The assessment year for any financial year is the year immediately following it, when the income earned in the financial year is assessed for tax. For the financial year 2017-18, the assessment year is 2018-19.

🎯 Exam Tip: Understand the difference between a financial year (when income is earned) and an assessment year (when income is taxed). This concept is fundamental to income tax.

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 ?
Solution:
Let the income of Shekhar be x.
Shekhar spends 60% of his income.
∴ Shekhar's expenditure = 60% of x
∴ Amount remaining with Shekhar = (100 - 60)% of x
= 40% of x
= 12 X X
= 0.4x
From the balance left, he donates Rs. 300 to an orphanage.
∴ Amount left with Shekhar = \( 0.4x - 300 \)
Now, the amount left with him is Rs. 3200.
∴ \( 3200 = 0.4x - 300 \)
∴ \( 0.4x = 3500 \)
\( x = \frac{3500}{0.4} \)
\( = \frac{3500 \times 10}{0.4 \times 10} \)
\( = \frac{35000}{4} \)
\( = 8750 \)
∴ The income of Mr. Shekhar is Rs. 8750.
Answer: Mr. Shekhar's income is Rs. 8750.
In simple words: Mr. Shekhar spent 60% of his income, then donated Rs. 300 from the remaining 40%, leaving him with Rs. 3,200. By setting up an equation, we find his total income.

🎯 Exam Tip: Break down word problems into percentages and equations. Carefully track the 'remaining amount' after each transaction to avoid errors.

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 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 ?
Solution:
Mr. Hiralal:
Amount invested by Mr. Hiralal in mutual fund = Rs. 2,15,000
Amount received by Mr. Hiralal = Rs. 3,05,000
∴ Mr. Hiralal's profit = Amount received - Amount invested
= \( 305000 - 215000 = \text{Rs. } 90000 \)
Mr. Hiralal's percentage of profit
\( = \frac{90000}{215000} \times 100 \)
\( = 41.86\% \)
Mr. Ramniklal:
P = Rs. 140000, R = 8%, n = 2 years
∴ Compound interest (I)
= A-P
\( = P \left( 1 + \frac{R}{100} \right)^n - P \)
\( = P \left[ \left( 1 + \frac{R}{100} \right)^n - 1 \right] \)
\( = 140000 \left[ \left( 1 + \frac{8}{100} \right)^2 - 1 \right] \)
\( = 140000 \left[ (1 + 0.08)^2 - 1 \right] \)
\( = 140000 \left[ (1.08)^2 - 1 \right] \)
\( = 140000(1.1664 - 1) \)
\( = 140000 \times 0.1664 \)
\( = \text{Rs. } 23296 \)
∴ Mr. Ramniklal's percentage of profit
\( = \frac{23296}{140000} \times 100 \)
\( = 16.64\% \)
∴ The percentage gains of Mr. Hiralal and Mr. Ramniklal are 41.86% and 16.64% respectively, and hence, Mr. Hiralal's investment was more profitable.
Answer: Mr. Hiralal's percentage gain is 41.86%, and Mr. Ramniklal's is 16.64%. Mr. Hiralal's investment was more profitable.
In simple words: To compare profitability, we calculate the percentage gain for each investment. Mr. Hiralal's profit is a simple calculation of received minus invested, while Mr. Ramniklal's requires using the compound interest formula. The higher percentage gain indicates more profitability.

🎯 Exam Tip: When comparing investments, always calculate the percentage gain or return on investment to get a standardized measure, rather than just the absolute profit. Remember the compound interest formula for these calculations.

Question 4. At the start of a year there were Rs. 24,000 in a savings account. After adding 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 ?
Solution:
Here, P = \( 24000 + 56000 \)
= Rs. 80000
R = 7.5%, n = 3 years
Total amount after 3 years
\( = P \left( 1 + \frac{R}{100} \right)^n \)
\( = 80000 \times \left( 1 + \frac{7.5}{100} \right)^3 \)
\( = 80000 (1 + 0.075)^3 \)
\( = 80000 (1.075)^3 \)
\( = 80000 \times 1.242297 \)
\( = 99383.76 \)
∴ The total amount after 3 years is 99383.76.
Answer: The total amount after 3 years will be Rs. 99383.76.
In simple words: First, calculate the principal amount by adding the initial savings and the new investment. Then, use the compound interest formula with the given rate and time period to find the total amount after 3 years.

🎯 Exam Tip: Accurately calculate the principal amount before applying the compound interest formula. Pay close attention to the interest rate (R) and the number of compounding periods (n) for correct calculation.

Question 5. Mr. Manohar gave 20% of his income to his elder son and 30% to his younger son. He gave 10% of the balance income as donation to a school. He still had Rs. 1,80,000 for himself. What was Mr. Manohar's income ?
Solution:
Let the income of Mr. Manohar be x.
Amount given to elder son = 20% of x
Amount given to younger son = 30% of x
Total amount given to both sons = \( (20 + 30)\% \) of x = 50% of x
∴ Amount remaining with Mr. Manohar = \( (100 - 50)\% \) of x
= 50% of x
\( = \frac{50}{100} \times x \)
= 0.5 x
He gave 10% of the balance income as donation to a school.
Amount donated to school = 10% of 0.5x
\( = \frac{10}{100} \times 0.5x \)
= 0.05x
∴ Amount remaining with Mr. Manohar after donating to school = \( 0.5x - 0.05x \)
= 0.45x
Mr. Manohar still had 1,80,000 for himself after donating to school.
∴ \( 180000 = 0.45x \)
\( x = \frac{180000}{0.45} \)
\( = \frac{180000 \times 100}{0.45 \times 100} \)
\( = \frac{18000000}{45} \)
\( = 400000 \)
∴ The income of Mr. Manohar is Rs. 4,00,000.
Answer: Mr. Manohar's income is Rs. 4,00,000.
In simple words: Mr. Manohar distributed parts of his income, then donated from the remaining amount, finally retaining Rs. 1,80,000. By calculating the percentages given at each step, we can set up an equation to find his total original income.

🎯 Exam Tip: When dealing with successive deductions from income, always calculate the remaining percentage after each step. Pay attention to whether a percentage is taken from the 'total income' or the 'balance income'.

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 ?
Solution:
Let the income of Kailash be x.
Kailash spends 85% of his income.
∴ Kailash's expenditure = 85% of x
\( = \frac{85}{100} \times x \)
= 0.85 x
Kailash's income increased by 36%.
∴ Kailash's new income = x + 36% of x
\( = x + \frac{36}{100} \times x \)
= x + 0.36x
= 1.36x
Kailash's expenses increased by 40%.
∴ Kailash's new expenditure = 0.85x + 40% of 0.85x
\( = 0.85x + \frac{40}{100} \times 0.85 \times 100 \)
= 0.85x + 0.4 \( \times \) 0.85x
= 0.85x (1 + 0.4)
= 0.85x \( \times \) 1.4
= 1.19x
∴ Kailash's new saving = Kailash's new income - Kailash's new expenditure
= \( 1.36x - 1.19x \)
= 0.17x
Percentage of Kailash's new saving
\( = \frac{0.17x}{1.36x} \times 100 \)
= 12.5%
∴ Kailash saves 12.5% of his new earning.
Answer: Kailash saves 12.5% of his new earning.
In simple words: We calculate Kailash's initial expenditure and then his new income and new expenditure based on the given percentage increases. Finally, we determine his new savings as a percentage of his new income.

🎯 Exam Tip: Be meticulous with calculations involving percentage increases. Clearly define original and new income/expenditure, then calculate savings before converting to a percentage.

Question 7. Total income of Ramesh, Suresh and Preeti is Rs. 8,07,000. 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.
Solution:
Let the annual income of Ramesh, Suresh and Preeti be x, y and z respectively.
Total income of Ramesh, Suresh and Preeti = Rs. 8,07,000
∴ \( x + y + z = 807000 \) ...(i)

∴ Savings of Ramesh = 25% of x
\( = \text{Rs. } \frac{25x}{100} \) ...(ii)
Savings of Suresh = 20% of y
\( = \text{Rs. } \frac{20y}{100} \) ...(iii)
Savings of Preeti = 10% of z
\( = \text{Rs. } \frac{10z}{100} \) .....(iv)
Ratio of their savings = 16 : 17 : 12
Let the common multiple be k.
Savings of Ramesh = Rs. 16 k ... (v)
Savings of Suresh = Rs. 17 k ... (vi)
Savings of Preeti = Rs. 12 k ... (vii)
∴ \( \frac{25x}{100} = 16k \) ...[From (ii) and (v)]

\( x = 16k \times \frac{100}{25} \)
∴ \( x = 64k \) ...(viii)
\( \frac{20y}{100} = 17k \) ...[From (iii) and (vi)]

\( y = 17k \times \frac{100}{20} \)
∴ \( y = 85k \) ...(ix)
\( \frac{10z}{100} = 12k \) ...[From (iv) and (vii)]

\( z = 12k \times \frac{100}{10} \)
∴ \( z = 120k \) ...(x)
From (i), (viii), (ix) and (x), we get
\( 64k + 85k + 120k = 807000 \)
\( 269k = 807000 \)
\( k = \frac{807000}{269} \)
\( k = 3000 \)
∴ Annual saving of Ramesh = \( 16k \)
\( = 16 \times 3000 \)
\( = \text{Rs. } 48,000 \)
Annual saving of Suresh = \( 17k \)
\( = 17 \times 3000 \)
\( = \text{Rs. } 51,000 \)
Annual saving of Preeti = \( 12k \)
\( = 12 \times 3000 \)
\( = \text{Rs. } 36,000 \)
The annual savings of Ramesh, Suresh and Preeti are Rs. 48,000, Rs. 51,000 and Rs. 36,000 respectively.
Answer: The annual saving of Ramesh is Rs. 48,000, Suresh is Rs. 51,000, and Preeti is Rs. 36,000.
In simple words: We used the given expense percentages to find each person's saving percentage. By setting these savings equal to a common multiple 'k' based on their saving ratio, we expressed each person's income in terms of 'k'. Substituting these into the total income equation allowed us to solve for 'k' and then find each person's individual saving.

🎯 Exam Tip: Systematically use variables for unknown incomes and express savings in two ways: as a percentage of income and as a multiple of the common ratio. This approach helps set up simultaneous equations for a complete solution.

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.
i. Mr. Kadam is 35 years old and his taxable income is Rs. 13,35,000.
Mr. Kadam's income is more than 10,00,000.
∴ Income tax = Rs. 1,12,500 + 30% of (taxable income - 10,00,000)
= Rs. 1,12,500 + 30% of (13,35,000 - 10,00,000)
\( = 112500 + \frac{30}{100} \times 335000 \)
\( = 112500 + 100500 \)
= Rs. 213000
Education cess = 2% of income tax
\( = \frac{2}{100} \times 213000 \)
= Rs. 4260.
Secondary and Higher Education cess
= 1% of income tax
\( = \frac{1}{100} \times 213000 \)
= 2130
Total income tax = Income tax + Education cess + Secondary and higher education cess
= \( 213000 + 4260 + 2130 = \text{Rs. } 2,19,390 \)
∴ Mr. Kadam will have to pay income tax of Rs. 2,19,390.
Answer: Mr. Kadam's total income tax payable is Rs. 2,19,390.
In simple words: Mr. Kadam's income falls into a tax bracket above Rs. 10,00,000. We calculate his basic tax, then add 2% education cess and 1% secondary and higher education cess to the basic tax to find the total tax.

🎯 Exam Tip: Know the income tax slabs and corresponding tax rates for different income groups. Remember to add education cess and secondary/higher education cess (which are percentages of the calculated income tax, not the income) to the total tax.

Question.
(ii) Mr. Khan is 65 years old and his taxable income is Rs. 4,50,000.
Answer: 
ii. Mr. Khan is 65 years old and his taxable income is Rs. 4,50,000.
Mr. Khan's income falls in the slab Rs. 3,00,001 to Rs. 5,00,000.
∴ Income tax
= 5% of (taxable income - 300000)
= 5% of (450000 - 300000)
\( = \frac{5}{100} \times 150000 \)
= Rs. 7500
Education cess = 2% of income tax
\( = \frac{2}{100} \times 7500 \)
= Rs. 150
Secondary and Higher Education cess = 1 % of income tax
\( = \frac{1}{100} \times 7500 \)
= 75
Total income tax = Income tax + Education cess + Secondary and higher education cess
= \( 7500 + 150 + 75 \)
= Rs. 7725
Mr. Khan will have to pay income tax of Rs. 7725.
Answer: Mr. Khan's total income tax payable is Rs. 7,725.
In simple words: Mr. Khan's income falls in the Rs. 3,00,001 to Rs. 5,00,000 bracket for senior citizens. We calculate 5% tax on the amount exceeding Rs. 3,00,000, then add education cess and secondary/higher education cess to find his total tax.

🎯 Exam Tip: Note that tax slabs and rates can differ for senior citizens. Always identify the correct age group and apply the corresponding tax rules and cess calculations.

Question.
(iii) Miss Varsha (Age 26 years) has a taxable income of Rs. 2,30,000.
Answer: 
iii. Taxable income = Rs. 2,30,000
age = 26 years
The yearly income of Miss Varsha is less than Rs. 2,50,000.
Hence, Miss Varsha will not have to pay income tax.
Answer: Miss Varsha will not have to pay any income tax.
In simple words: Miss Varsha's age is 26 years, and her taxable income is Rs. 2,30,000. Since this amount is below the basic exemption limit of Rs. 2,50,000 for individuals below 60 years of age, she is not required to pay income tax.

🎯 Exam Tip: Always check the basic exemption limit for income tax, which varies based on age (e.g., below 60, senior citizens, super senior citizens). An income below this limit results in no income tax liability.

Maharashtra Board Class 9 Maths Chapter 6 Financial Planning Problem Set 6 Intext Questions And Activities

Question 1. With your parent's help write down the income and expenditure of your family for one week. Make 7 columns for the seven days of the week. Write all expenditure under such heads as provisions, education, medical expenses, travel, clothes and miscellaneous. On the credit side write the amount received for daily expenses, previous balance and any other new income. (Textbook pg. no. 98)
Answer:
In simple words: This activity requires you to create a detailed financial record for your family over one week, listing all income sources and categorizing all expenses daily. This helps in understanding family budgeting.

🎯 Exam Tip: This question is an activity, not a theoretical problem. Focus on practical application to understand real-world financial tracking. No specific exam marks are tied to this, but the understanding gained is valuable.

Question 2. In the holidays, write the accounts for the whole month. (Textbook pg. no. 98)
Answer:
In simple words: This activity is a monthly extension of the weekly income and expenditure tracking. It's about maintaining a complete financial log for your family during a holiday month.

🎯 Exam Tip: This is a practical exercise to build budgeting skills. Ensure all income and expenditure are recorded accurately to understand the monthly financial flow. No specific exam marks are tied to this, but the understanding gained is valuable.

Question 3. What is a tax? Which are different types of taxes? Find out more information on following websites
www.incometaxindia.gov.in,
www.mahavat.gov.in
www.gst.gov.in (Textbook pg. no. 99)
Answer:
In simple words: Taxes are compulsory financial contributions imposed by a government on individuals or entities to fund public services. There are various types, broadly direct (like income tax) and indirect (like GST). Researching the provided websites will give detailed information on Indian taxes.

🎯 Exam Tip: For theoretical questions on taxes, define what tax is and list major types (direct/indirect, income tax, GST, property tax). Understanding the purpose and sources of tax revenue is key.

Question 4. Obtain more information about different types of taxes from employees and professionals who pay taxes. (Textbook pg. no. 99)
Answer:
In simple words: This activity involves interviewing people who pay taxes to gain practical insights into the tax system. This can reveal details about how taxes affect different professions and income levels.

🎯 Exam Tip: This is a research activity; there's no single correct answer for an exam. The goal is to develop an understanding of real-world tax applications and impacts on different individuals and professions.

Question 5. Obtain information about sections 80C, 80G, 80D of the Income Tax Act. (Textbook pg. no. 103)
Answer:
In simple words: This research task focuses on specific sections of the Income Tax Act that allow for deductions. Section 80C covers investments like PPF and ELSS, 80G covers donations, and 80D covers health insurance premiums, all reducing taxable income.

🎯 Exam Tip: For exam purposes, know the key deductions available under these common sections (80C, 80G, 80D). Understand what each section allows you to claim a deduction for and their respective limits.

Question 6. Study a PAN card and make a note of all the information it contains. (Textbook pg.no. 103)
Answer:
In simple words: A PAN (Permanent Account Number) card is a unique 10-digit alphanumeric identifier issued by the Indian Income Tax Department. It typically contains the cardholder's name, father's name, date of birth, photograph, signature, and the unique PAN.

🎯 Exam Tip: Understand the purpose of a PAN card as a primary identification for financial transactions in India. Be able to list the key information present on a PAN card for practical knowledge.

Question 7. Obtain information about all the devices and means used for carrying out cash-minus transactions. (Textbook pg, no, 103)
Answer:
In simple words: Cash-minus transactions refer to digital or cashless payment methods. These include debit cards, credit cards, mobile wallets (like Google Pay, Paytm), UPI (Unified Payments Interface), internet banking, NEFT/RTGS, and QR code payments.

🎯 Exam Tip: Be familiar with common cashless transaction methods. For an exam, be able to list and briefly describe popular digital payment instruments and technologies used in the modern financial system.

Question 8. Visit www.incometaxindia.gov.in which is a website of the Government of India. Click on the 'incometax calculator' menu. Fill in the form that gets downloaded using an imaginary income and imaginary deductible amounts and try to compute the income tax payable for this income. (Textbook pg.no. 107)
Answer: 
In simple words: This activity requires you to use the online income tax calculator on the official Indian income tax website. You will input hypothetical income and deduction figures to simulate tax calculation, understanding how the system works. Students should attempt the above activities on their own.

🎯 Exam Tip: This is a hands-on activity to understand the practical application of income tax calculations. While not a direct exam question, performing this activity enhances your understanding of tax computation, which is crucial for related problems.