Std 9 Mathematics Part 1 · Chapter 6

6. Financial Planning

Solutions to Practice Sets 6.1, 6.2 and Problem Set 6, with step-by-step working. Maharashtra State Board (Balbharati), Standard Nine Mathematics Part 1 (Algebra).

Practice Set 6.1

1Alka spends 90% of the money that she receives every month, and saves Rs. 120. How much money does she get monthly?

She saves 100% − 90% = 10% of her money.

10% of x = 120 ⇒ x = 120 × 10010 = 1200

Rs. 1200 per month

2Sumit 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?

Loss in first year = 20% of 50,000 = 10,000. Remaining capital = 40,000

Profit in sweets business = 5% of 40,000 = 2,000. Capital now = 42,000

Compared with the original capital: 50,000 − 42,000 = 8,000 (loss)

Loss percent = 8,00050,000 × 100 = 16%

Loss of Rs. 8,000, i.e. 16% of the original capital

3Nikhil 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?

Total used = 5% + 14% + 3% + 40% = 62%. Balance = 38% of income

38% of x = 19,000 ⇒ x = 19,000 × 10038 = 50,000

Rs. 50,000

4Mr. 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?

Mr. Sayyad

Compound interest = P[(1 + r100)ⁿ − 1] = 40,000[(1.08)² − 1]

= 40,000 [1.1664 − 1] = 40,000 × 0.1664 = 6,656 rupees

Percent gain = 6,65640,000 × 100 = 16.64%

Mr. Fernandes

Gain = 1,92,000 − 1,20,000 = 72,000 rupees

Percent gain = 72,0001,20,000 × 100 = 60%

Mr. Fernandes’s investment was more profitable (60% against 16.64%)

5Sameera spent 90% of her income and donated 3% for socially useful causes. If she was left with Rs. 1750 at the end of the month, what was her actual income?

Spent and donated = 90% + 3% = 93%. Left = 7% of income

7% of x = 1750 ⇒ x = 1750 × 1007 = 25,000

Rs. 25,000

Practice Set 6.2

These answers use the sample tax tables printed in the textbook (Table I: up to 60 years, Table II: 60 to 80 years, Table III: above 80 years, with 2% education cess and 1% secondary and higher education cess). Actual income-tax rules change every year in the budget.

1Observe the table given below. Check and decide, whether the individuals have to pay income tax.

No.	Individual	Age	Taxable income (₹)	Exemption limit (₹)	Pays income tax?
(i)	Miss Nikita	27	2,34,000	2,50,000	No
(ii)	Mr. Kulkarni	36	3,27,000	2,50,000	Yes
(iii)	Miss Mehta	44	5,82,000	2,50,000	Yes
(iv)	Mr. Bajaj	64	8,40,000	3,00,000	Yes
(v)	Mr. Desilva	81	4,50,000	5,00,000	No

Tax is payable only when the taxable income is more than the basic exemption limit for the person’s age group.

2Mr. 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 and donated Rs. 12,000 to the PM’s Relief Fund. Compute his income tax.

Annual income = 42,000 × 12 = 5,04,000 rupees

Deduction under 80C = GPF (3000 × 12 = 36,000) + NSC 15,000 = 51,000 rupees (within the limit of 1,50,000)

Deduction under 80G (PM’s Relief Fund) = 12,000 rupees

Taxable income = 5,04,000 − (51,000 + 12,000) = 4,41,000 rupees

Age 48 ⇒ Table I, slab 2,50,001 to 5,00,000. Income tax = 5% of (4,41,000 − 2,50,000) = 5% of 1,91,000 = 9,550 rupees

Education cess = 2% of 9,550 = 191; Secondary and higher education cess = 1% of 9,550 = 95.50

Total income tax = 9,550 + 191 + 95.50 = 9,836.50 rupees

Income tax payable = Rs. 9,836.50

Problem Set 6

1Write 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) 1,50,000 rupees
(ii) A person has earned his income during the financial year 2017-18. Then his assessment year is — (B) 2018-19
The assessment year is the year immediately after the financial year.

2Mr. 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?

Balance after spending = 40% of income

40% of x − 300 = 3,200 ⇒ 40% of x = 3,500 ⇒ x = 3,500 × 10040 = 8,750

Rs. 8,750

3Mr. 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?

Hiralal: gain = 3,05,000 − 2,15,000 = 90,000; percent gain = 90,0002,15,000 × 100 ≈ 41.86%

Ramniklal: compound interest = 1,40,000[(1.08)² − 1] = 1,40,000 × 0.1664 = 23,296; percent gain = 16.64%

Hiralal: 41.86% Ramniklal: 16.64% Hiralal’s investment was more profitable.

4At 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?

Principal = 24,000 + 56,000 = 80,000 rupees

A = P(1 + r100)ⁿ = 80,000 × (1.075)³

(1.075)³ = 1.242296875 ⇒ A = 80,000 × 1.242296875 = 99,383.75

Rs. 99,383.75

5Mr. 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?

Given to sons = 20% + 30% = 50%. Balance = 50% of income

Donation = 10% of the balance, so he keeps 90% of the balance = 90% of 50% = 45% of income

45% of x = 1,80,000 ⇒ x = 1,80,000 × 10045 = 4,00,000

Rs. 4,00,000

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?

Let the earlier income = 100. Earlier expenses = 85

New income = 100 + 36 = 136. New expenses = 85 + 40% of 85 = 85 + 34 = 119

New savings = 136 − 119 = 17

Percentage saved = 17136 × 100 = 12.5%

He now saves 12.5% of his income

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.

They save 25%, 20% and 10% of their incomes. Let the savings be 16k, 17k and 12k.

Incomes: Ramesh = 16k × 10025 = 64k; Suresh = 17k × 10020 = 85k; Preeti = 12k × 10010 = 120k

64k + 85k + 120k = 8,07,000 ⇒ 269k = 8,07,000 ⇒ k = 3,000

Savings: 16 × 3,000 = 48,000; 17 × 3,000 = 51,000; 12 × 3,000 = 36,000

Ramesh: Rs. 48,000 Suresh: Rs. 51,000 Preeti: Rs. 36,000

(Their incomes are Rs. 1,92,000, Rs. 2,55,000 and Rs. 3,60,000.)

8Compute 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.

Table I, slab above 10,00,000: Income tax = 1,12,500 + 30% of (13,35,000 − 10,00,000)

= 1,12,500 + 30% of 3,35,000 = 1,12,500 + 1,00,500 = 2,13,000

Education cess = 2% of 2,13,000 = 4,260; S&H education cess = 1% of 2,13,000 = 2,130

Total = 2,13,000 + 4,260 + 2,130 = 2,19,390

Rs. 2,19,390

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

Table II (senior citizen), slab 3,00,001 to 5,00,000: Income tax = 5% of (4,50,000 − 3,00,000) = 5% of 1,50,000 = 7,500

Education cess = 2% of 7,500 = 150; S&H education cess = 1% of 7,500 = 75

Total = 7,500 + 150 + 75 = 7,725

Rs. 7,725

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

Table I: taxable income up to 2,50,000 is exempt. No income tax is payable

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