Maharashtra Board Class 10 Maths Chapter 4 Financial Planning Set 4.B Solutions

Question 1. Write the correct alternative for the following questions.
(i) If the Face Value of a share is Rs. 100 and Market value is Rs. 75, then which of the following statement is correct?
(A) The share is at premium of Rs. 175
(B) The share is at discount of Rs. 25
(C) The share is at premium of Rs. 25
(D) The share is at discount of Rs. 75
Answer: (B)
In simple words: When the market value of a share is less than its face value, the share is said to be at a discount. Here, Market Value (Rs. 75) is less than Face Value (Rs. 100), so it's a discount of Rs. 25.

🎯 Exam Tip: Remember that a discount occurs when MV < FV, and a premium occurs when MV > FV. The difference (FV - MV or MV - FV) is the amount of discount or premium.

(ii) What is the amount of dividend received per share of face value Rs. 10 if dividend declared is 50%.
(A) Rs. 50
(B) Rs. 5
(C) Rs. 500
(D) Rs. 100
Answer: Dividend \( = 10 \times \frac{50}{100} = \text{Rs. } 5 \)
(B)
In simple words: Dividend is always calculated on the face value of the share. A 50% dividend on a face value of Rs. 10 means 50% of Rs. 10, which is Rs. 5.

🎯 Exam Tip: Always calculate dividends on the Face Value (FV) of the share, not the Market Value (MV), unless specified otherwise. This is a common point of confusion.

(iii) The NAV of a unit in mutual fund scheme is Rs. 10.65, then find the amount required to buy 500 such units.
(A) 5325
(B) 5235
(C) 532500
(D) 53250
Answer: (A)
In simple words: The total amount needed to buy mutual fund units is the Net Asset Value (NAV) per unit multiplied by the number of units purchased. So, Rs. 10.65 per unit for 500 units equals Rs. 5325.

🎯 Exam Tip: For mutual funds, the purchase amount is directly calculated by multiplying the NAV per unit by the number of units desired. There are no additional concepts like Face Value or Premium/Discount here.

(iv) Rate of GST on brokerage is _____
(A) 5%
(B) 12%
(C) 18%
(D) 28%
Answer: (C)
In simple words: The standard Goods and Services Tax (GST) rate applicable on brokerage services for financial transactions in India is 18%.

🎯 Exam Tip: This is a factual recall question. Knowing the standard GST rate for brokerage (18%) is important for calculations involving share trading costs.

(v) To find the cost of one share at the time of buying the amount of Brokerage and GST is to be _____ MV of share.
(A) added to
(B) subtracted from
(C) Multiplied with
(D) divided by
Answer: (A)
In simple words: When buying a share, the total cost includes the market value of the share plus any additional charges like brokerage and GST on brokerage, as these are expenses incurred.

🎯 Exam Tip: Remember that brokerage and GST are always added to the market value when buying shares, as they are part of the total cost of acquisition. When selling, these costs are subtracted from the selling price.

Question 2. Find the purchase price of a share of FV Rs. 100 if it is at premium of Rs. 30. The brokerage rate is 0.3%.
Solution:
Here, Face Value of share = Rs. 100,
premium = Rs. 30, brokerage = 0.3%
MV = FV + Premium
= 100 + 30
= Rs. 130
Brokerage = 0.3% of MV
\( = \frac{0.3}{100} \times 130 = \text{Rs. } 0.39 \)
Purchase price of a share = MV + Brokerage
= 130 + 0.39
= Rs. 130.39
Purchase price of a share is Rs. 130.39.
In simple words: The market value of a share at a premium is its face value plus the premium. To find the total purchase price, you add the brokerage (calculated on the market value) to this market value.

🎯 Exam Tip: Always calculate market value first (FV + Premium or FV - Discount). Then, calculate brokerage on the market value, and finally add this brokerage to the market value to get the total purchase price.

Question 3. Prashant bought 50 shares of FV Rs. 100, having MV Rs. 180. Company gave 40% dividend on the shares. Find the rate of return on investment.
Solution:
Here, Number of shares = 50, FV = Rs. 100,
MV = Rs. 180, rate of dividend = 40%
\( \therefore \) Sum invested = Number of shares \( \times \) MV
= 50 \( \times \) 180
= Rs. 9000
Dividend per share = 40% of FV
\( = \frac{40}{100} \times 100 \)
Dividend = Rs. 40
\( \therefore \) Total dividend on 50 shares = 50 \( \times \) 40
= Rs. 2000
Now, rate of return \( = \frac{\text{Total dividend}}{\text{Sum invested}} \times 100 \)
\( = \frac{2000}{9000} \times 100 \)
= 22.2%
\( \therefore \) Rate of return on investment is 22.2%.
In simple words: First, calculate the total investment by multiplying the number of shares by their market value. Then, calculate the total dividend received (dividend rate on face value multiplied by the number of shares). Finally, divide the total dividend by the total investment and multiply by 100 to get the rate of return.

🎯 Exam Tip: Rate of return is a key performance indicator. Remember the formula: (Total Dividend / Sum Invested) × 100. Be careful to use FV for dividend calculation and MV for sum invested calculation.

Question 4. Find the amount received when 300 shares of FV Rs. 100, were sold at a discount of Rs. 30.
Solution:
Here, FV = Rs. 100, number of shares = 300,
discount = Rs. 30
MV of 1 share = FV - Discount
= 100 - 30 = Rs. 70
\( \therefore \) MV of 300 shares = 300 \( \times \) 70
= Rs. 21,000
\( \therefore \) Amount received is Rs. 21,000.
In simple words: When shares are sold at a discount, their market value is the face value minus the discount amount. The total amount received is then the market value per share multiplied by the number of shares sold.

🎯 Exam Tip: For selling shares at a discount, the Market Value (MV) is calculated as Face Value (FV) - Discount. Ensure you multiply this MV by the total number of shares to get the final amount received.

Question 5. Find the number of shares received when Rs. 60,000 was invested in the shares of FV Rs. 100 and MV Rs. 120.
Solution:
Here, FV = Rs. 100, MV = Rs. 120,
Sum invested = Rs. 60,000
Number of shares \( = \frac{\text{Sum invested}}{\text{MV}} \)
\( = \frac{60,000}{120} \)
= 500
\( \therefore \) Number of shares received were 500.
In simple words: To find out how many shares can be bought with a certain investment, divide the total sum invested by the market value of one share.

🎯 Exam Tip: The number of shares purchased is always calculated using the total investment and the Market Value (MV) per share, not the Face Value (FV).

Question 6. Smt. Mita Agrawal invested Rs. 10,200 when MV of the share is Rs. 100. She sold 60 shares when the MV was Rs. 125 and sold remaining shares when the MV was Rs. 90. She paid 0.1% brokerage for each trading. Find whether she made profit or loss? and how much?
Solution:
For purchasing shares:
Here, sum invested = Rs. 10,200, MV = Rs. 100
\( \therefore \) No. of shares \( = \frac{\text{Sum invested}}{\text{MV}} \)
\( = \frac{10,200}{100} \)
= 102
Brokerage = 0.1% of sum invested
\( = \frac{0.1}{100} \times 10200 = \text{Rs. } 10.2 \)
\( \therefore \) Purchase value of 102 shares
= sum invested + brokerage
= 10200 + 10.2
= Rs. 10210.2
For selling shares:
60 shares sold at MV of Rs. 125.
\( \therefore \) MV of 60 shares = 125 \( \times \) 60
= Rs. 7500
Brokerage \( = \frac{0.1}{100} \times 7500 = \text{Rs. } 7.5 \)
\( \therefore \) Sale value of 60 shares = 7500 - 7.5 = Rs. 7492.5
Now, remaining shares = 102 - 60 = 42
But 42 shares sold at MV of Rs. 90.
\( \therefore \) MV of 42 shares = 42 \( \times \) 90 = Rs. 3780
\( \therefore \) Brokerage \( = \frac{0.1}{100} \times 3780 = \text{Rs. } 3.78 \)
\( \therefore \) Sale value of 42 shares = 3780 - 3.78 = Rs. 3776.22
Total sale value = 7492.5 + 3776.22 = Rs. 11268.72
Since, Purchase value < Sale value
\( \therefore \) Profit is gained.
\( \therefore \) Profit = Sale value - Purchase value
= 11268.72 - 10210.2
= Rs. 1058.52
\( \therefore \) Smt. Mita Agrawal gained a profit of Rs. 1058.52.
In simple words: Calculate the total shares purchased and the total purchase value (including brokerage). Then, calculate the sale value for each batch of shares sold, subtracting brokerage from each. Sum up all sale values. Compare the total sale value with the total purchase value to determine profit or loss.

🎯 Exam Tip: Pay close attention to brokerage calculations for both buying and selling. Brokerage is added to MV for buying and subtracted from MV for selling. Also, track the remaining shares carefully if sales happen in batches.

Question 7. Market value of shares and dividend declared by the two companies is given below. Face value is same and it is Rs. 100 for both the shares. Investment in which company is more profitable?
(i) Company A - Rs. 132,12%
(ii) Company B - Rs. 144,16%
Solution:
For company A:
FV = Rs. 100, MV = Rs. 132,
Rate of dividend = 12%
Dividend = 12% of FV
\( = \frac{12}{100} \times 100 = \text{Rs. } 12 \)
Rate of return \( = \frac{\text{Dividend}}{\text{Sum invested}} \times 100 \)
\( = \frac{12}{132} \times 100 \)
= 9.09%
For company B:
FV = Rs. 100, MV = Rs. 144,
\( \bullet \) Rate of dividend = 16%
Dividend = 16% of FV
\( = \frac{16}{100} \times 100 \)
= Rs. 16
Rate of return \( = \frac{\text{Dividend}}{\text{Sum invested}} \times 100 \)
\( = \frac{16}{144} \times 100 \)
= 11.11%
\( \therefore \) Rate of return of company B is more.
\( \therefore \) Investment in company B is more profitable.
In simple words: To compare profitability, calculate the rate of return for each company. The rate of return is the dividend per share divided by the market value per share, multiplied by 100. The company with a higher rate of return is more profitable.

🎯 Exam Tip: Profitability comparison requires calculating the "Rate of Return". This involves (Dividend per share / Market Value per share) * 100. Always use Face Value for dividend calculation and Market Value for the invested amount.

Question 8. Shri. Aditya Sanghavi invested Rs. 50,118 in shares of FV Rs. 100, when the market value is Rs. 50. Rate of brokerage is 0.2% and Rate of GST on brokerage is 18%, then How many shares were purchased for Rs. 50,118?
Solution:
Here, FV = Rs. 100, MV = Rs. 50
Purchase value of shares = Rs. 50118,
Rate of brokerage = 0.2%, Rate of GST = 18%
Brokerage = 0.2% of MV
\( = \frac{0.2}{100} \times 50 \)
Brokerage = Rs. 0.1
GST = 18% of brokerage
\( = \frac{18}{100} \times 0.1 \)
= 0.018
Purchase value of a share
= MV + Brokerage + GST
= 50 + 0.1 + 0.018
= 50.118
\( \therefore \) Number of shares \( = \frac{\text{Purchase value of all shares}}{\text{Purchase value of one share}} \)
\( = \frac{50118}{50.118} \)
= 1000
\( \therefore \) 1000 shares were purchased for Rs. 50,118.
In simple words: First, calculate the cost of one share by adding its market value, brokerage (on MV), and GST (on brokerage). Then, divide the total investment by this per-share cost to find the total number of shares purchased.

🎯 Exam Tip: When calculating the purchase price per share, remember to add both brokerage (calculated on MV) and GST (calculated on brokerage) to the Market Value. This sum is the true cost of acquiring one share.

Question 9. Shri. Batliwala sold shares of Rs. 30,350 and purchased shares of Rs. 69,650 in a day. He paid brokerage at the rate of 0.1% on sale and purchase. 18% GST was charged on brokerage. Find his total expenditure on brokerage and tax.
Solution:
Total amount = sale value + Purchase value
= 30350 + 69650
= Rs. 1,00,000
Rate of Brokerage = 0.1 %
Brokerage = 0.1% of 1,00,000
\( = \frac{0.1}{100} \times 1,00,000 \)
= Rs. 100
Rate of GST = 18%
\( \therefore \) GST = 18 % of brokerage
\( = \frac{18}{100} \times 100 \)
\( \therefore \) GST = Rs. 18
Total expenditure on brokerage and tax
= 100 + 18 = Rs. 118
\( \therefore \) Total expenditure on brokerage and tax is Rs. 118.
In simple words: Calculate the total transaction value (sales + purchases). Then, compute the total brokerage as a percentage of this value. Finally, calculate GST as a percentage of the total brokerage, and sum brokerage and GST for the total expenditure.

🎯 Exam Tip: This question simplifies brokerage calculation by applying it to the combined total transaction value. Ensure you calculate GST on the brokerage amount, not the total transaction value.

Alternate Method:
Brokerage = 0.1 %, GST = 18%
At the time of selling shares:
Total sale amount of shares = Rs. 30,350
Brokerage = 0.1% of 30,350
\( = \frac{0.1}{100} \times 30,350 \)
= Rs. 30.35
GST = 18% of Rs. 30.35
\( = \frac{18}{100} \times 30.35 \)
= Rs. 5.463
For purchasing shares:
Total purchase amount of shares = Rs. 69,650
Brokerage = 0.1% of 69,650
\( = \frac{0.1}{100} \times 69650 \)
= Rs. 69.65
GST = 18% of 69.65
\( = \frac{18}{100} \times 69.65 \)
= Rs. 12.537
\( \therefore \) Total expenditure on brokerage and tax = Brokerage and tax on selling +
Brokerage and tax on purchasing
= (30.35 + 5.463) + (69.65 + 12.537)
= Rs. 118
\( \therefore \) Total expenditure on brokerage and tax is Rs. 118.

Question 10. Sint. Aruna Thakkar purchased 100 shares of FV Rs. 100 when the MV is Rs. 1200. She paid brokerage at the rate of 0.3% and 18% GST on brokerage. Find the following-
(i) Net amount paid for 100 shares.
(ii) Brokerage paid on sum invested.
(iii) GST paid on brokerage.
(iv) Total amount paid for 100 shares.
Solution:
Here, FV = Rs. 100,
Number of shares = 100, MV = Rs. 1200
Brokerage = 0.3%, GST = 18%
(i) Sum invested = Number of shares \( \times \) MV
= 100 \( \times \) 1200 = Rs. 1,20,000
\( \therefore \) Net amount paid for 100 shares is Rs. 1,20,000.
(ii) Brokerage = 0.3% of sum invested
\( = \frac{0.3}{100} \times 1,20,000 = \text{Rs. } 360 \)
\( \therefore \) Brokerage paid on sum invested is Rs. 360.
(iii) GST = 18% of brokerage
\( = \frac{18}{100} \times 360 = \text{Rs. } 64.80 \)
\( \therefore \) GST paid on brokerage is Rs. 64.80.
(iv) Total amount paid for 100 shares
= Sum invested + Brokerage + GST
= 1,20,000 + 360 + 64.80
= Rs. 1,20,424.80
\( \therefore \) Total amount paid for 100 shares is Rs. 1,20,424.80.
In simple words: First, calculate the total investment based on the number of shares and market value. Then, determine the brokerage as a percentage of this investment. Next, calculate the GST as a percentage of the brokerage. Finally, sum up the investment, brokerage, and GST to get the total amount paid.

🎯 Exam Tip: Break down the problem into individual components as asked. Remember that brokerage is on the sum invested (MV x no. of shares), and GST is on the brokerage amount. Total cost is MV + Brokerage + GST.

Question 11. Smt. Anagha Doshi purchased 22 shares of FV Rs. 100 for Market Value of Rs. 660. Find the sum invested. After taking 20% dividend, she sold all the shares when market value was Rs. 650. She paid 0.1% brokerage for each trading done. Find the percent of profit or loss in the share trading. (Write your answer to the nearest integer)
Solution:
For purchasing shares:
Here, FV = Rs. 100, MV = Rs. 660, Number of shares = 22, rate of brokerage = 0.1%
Sum invested = MV \( \times \) Number of shares
= 660 \( \times \) 22
= Rs. 14,520
Brokerage = 0.1% of sum invested
\( = \frac{0.1}{100} \times 14520 = \text{Rs. } 14.52 \)
\( \therefore \) Amount invested for 22 shares
= Sum invested + Brokerage
= 14520 + 14.52
= Rs. 14534.52
For dividend:
Rate of dividend = 20%
\( \therefore \) Dividend per share = 20 % of FV
\( = \frac{20}{100} \times 100 = \text{Rs. } 20 \)
\( \therefore \) Dividend of 22 shares = 20 \( \times \) 22
= Rs. 440
For selling shares:
MV = 650, rate of brokerage = 0.1%
MV of 22 shares = 22 \( \times \) 650
= Rs. 14300
Brokerage = 0.1% of 14300
\( = \frac{0.1}{100} \times 14300 = \text{Rs. } 14.30 \)
\( \therefore \) Smt. Anagha income
= Dividend + MV of 22 shares - Brokerage
= 440 + 14300 - 14.30
= Rs. 14725.7
Since, income > Amount invested
Profit is gained.
Profit = Income - Amount invested
= 14725.7 - 14534.52
= Rs. 191.18
Profit Percentage \( = \frac{\text{Profit}}{\text{Amount invested}} \times 100 \)
\( = \frac{191.18}{14534.52} \times 100 = 1.31\% \)
\( \therefore \) Percentage of profit in the share trading is 1% (nearest integer).
In simple words: First, calculate the total investment (MV + brokerage). Then, determine the total income from selling (MV - brokerage) and the total dividend received. Compare the total income (sales proceeds + dividend) with the total investment to find the profit or loss, and then express it as a percentage of the initial investment.

🎯 Exam Tip: This is a multi-step problem. Calculate investment and dividend separately, then selling proceeds. Remember brokerage is added during buying and subtracted during selling. Dividend is always on FV. Finally, calculate profit/loss percentage relative to the *total investment*.

Alternate Method:
For purchasing share:
Here, FV = Rs. 100, MV = Rs. 660, Number of shares = 22, rate of brokerage = 0.1%
Sum invested = MV \( \times \) Number of shares
= 660 \( \times \) 22
= Rs. 14,520
Brokerage = 0.1% of MV
\( = \frac{0.1}{100} \times 660 = \text{Rs. } 0.66 \)
Amount invested for 1 share = 660 + 0.66
= Rs. 660.66
For dividend:
Rate of dividend = 20%
Dividend = 20% of FV \( = \frac{20}{100} \times 100 = \text{Rs. } 20 \)
For selling share:
MV = 650, rate of brokerage = 0.1%
Brokerage = 0.1 % of MV
\( = \frac{0.1}{100} \times 650 = \text{Rs. } 0.65 \)
Amount received after selling 1 share
= 650 - 0.65 = 649.35
\( \therefore \) Amount received including divided
= selling price of 1 share + dividend per share
= 649.35 + 20
= Rs. 669.35
Since, income > Amount invested
\( \therefore \) Profit is gained.
\( \therefore \) profit = 669.35 - 660.66 = Rs. 8.69
Profit Percentage \( = \frac{8.69}{660.66} \times 100 = 1.31\% \)
\( \therefore \) Percentage of profit in the share trading is 1 % (nearest integer).