# Shares and Dividend Class 10 RS Aggarwal Goyal Brothers ICSE Maths Solutions Ch-3

Shares and Dividend Class 10 RS Aggarwal Goyal Brothers Prakashan ICSE Foundation Maths Solutions Ch-3. Step by step solutions of exercise-3 questions as latest prescribe guideline for upcoming exam. Visit official Website CISCE for detail information about ICSE Board Class-10.

## Shares and Dividend Class 10 RS Aggarwal Goyal Brothers Prakashan ICSE Foundation Maths Solutions Ch-3

 Board ICSE Publications Goyal Brothers Prakashan Subject Maths Class 10th Chapter-3 Shares and Dividend Writer RS Aggarwal Book Name Foundation Topics Solution of Exe-3 Questions Edition 2024-2025

### Solution of Exe-3 Questions

Shares and Dividend Class 10 RS Aggarwal Goyal Brothers Prakashan ICSE Foundation Maths Solutions Ch-3

Page- 29,30,31

#### Exercise- 3

##### Que-1: Find the market value of : (i) 350, Rs100 shares at the premium of Rs8   (ii) 240, Rs50 shares at the discount of Rs5.

Solution- (i) Face value (FV) = Rs100 Premium = Rs8
So, Market value per share = Rs100 + Rs8 = Rs108
Now, to find the market value of 350 shares, we multiply the market value per share by the number of shares:
Market value of 350 shares = 350 * Rs108 = Rs37,800 Ans.

(ii) Number of Shares (N) = 240
Face Value (FV) = Rs50
Discount (D) = Rs5
Using the formula:
Market Value = 240 × (50 – 5)
Market Value = 240 × 45
Market Value = Rs10,800 Ans.

##### Que-2: Find the annual income from 450, Rs25 shares, paying 12% dividend.

Solution- Number of Shares (N) = 450
Face Value (FV) = Rs25
Dividend Rate = 12%
Dividend per Share = Face Value × Dividend Rate
= Rs25 × 12% = Rs3
Annual Income = Number of Shares × Dividend per Share
= 450 × Rs3 = Rs1350 Ans.

##### Que-3: A man wants to buy 600 shares available at Rs125 having the par value Rs100. (i) How much does he invest?   (ii) If the dividend is 8% per annum, what will be his annual income ?   (iii) If he wants to increase his annual income by Rs800, how many extra shares should he buy?

Solution- (i) Number of Shares (N) = 600
Market Price per Share = Rs125
Total Investment = 600 × Rs125
= Rs75,000 Ans.

(ii) Dividend per share = Par value of share × Dividend rate
= Rs100 × 8% = Rs8
Total dividend income = Number of shares × Dividend per share
= 600 shares × Rs8
= Rs4800 Ans.

(iii) Additional Annual Income Required = Rs800
Dividend per Share = Face Value × Dividend Rate
= Rs100 × 8%
= Rs8
Additional Shares Needed = Additional Annual Income Required / Dividend per Share
= Rs800 / Rs8
= 100 shares Ans.

##### Que-4: A man invests Rs22500 in Rs50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate : (i) the number of shares purchased   (ii) the annual dividend received (iii) the rate of return he gets on his investment.

Solution- (i) Amount invested = Rs22500
Face value per share = Rs50
Discount = 10%
Discounted Price per Share = Face Value – (Discount/100) * Face Value
= Rs50 – (10/100) * Rs50
= Rs50 – Rs5
= Rs45
Number of shares purchased = Amount invested / Discounted Price per Share
= Rs22500 / Rs45
= 500 shares Ans.

(ii) Number of shares purchased = 500
Face value per share = Rs50
Dividend rate = 12%
Annual Dividend Received = Number of shares × Face value per share × Dividend rate
= 500 shares × Rs50 × 12%
= 500 shares × Rs50 × 0.12
= Rs3000 Ans.

(iii) Rate of Return = (Annual Dividend Received / Amount invested) * 100
= (Rs3000 / Rs22500) * 100
= 0.1333 * 100
≈ 13.33% = 13% Ans.

##### Que-5: Find the market price of 12%, Rs25 shares of a company which pays a dividend of Rs1875 on an investment of Rs 20000.

Solution-  Nominal value (N.V.) = ₹ 25
Income (dividend) on one share = 12 % of N.V.
= (12/100)×25 = 3
Total income = ₹ 1875
⇒ No. of shares × Income on one share = 1875
⇒ No. of shares × 3 = 1875
⇒ No. of shares = 1875/3 = 625.
⇒ Sum invested = M.V. of each share × No. of shares
⇒ 20000 = M.V. of each share × 625
⇒ M.V. of each share = 20000/625 = ₹ 32 Ans.

##### Que-6: Mr. Ram Gopal invested Rs8000 in 7%, Rs100 shares at Rs80. After a year, he sold these shares at Rs75 each and invested the proceeds (including his dividend) in 18%, Rs25 shares at Rs41. Find : (i) his dividend for the first year   (ii) his annual income in the second year  (iii) the percentage increase in his return on his original investment.

Solution- (i) Number of shares bought by Mr. Ram Gopal
= 8000/80 = 100
Total face value of 100 shares = Rs 100 × 100 = Rs 10,000
Dividend = 7% of Rs 10,000 = (7/100) × 10,000 = Rs 700 Ans.
(ii) Amount received on selling 100 shares for Rs 75 each = Rs 100 × 75 = Rs 7500
Proceeds (including his dividend) = Rs 7500 + Rs 700 = Rs 8200
Number of shares of Rs 25 at Rs 41 = 820041 = 200
Total face value of 200 shares = Rs 25 × 200 = Rs 5000
Dividend = 18% of Rs 5000 = Rs18100 × 5000 = Rs 900 Ans.
(iii) Increase in income = Rs 900 – Rs 700 = Rs 200
∴%Increase in the return = (200/8000)×100 = 2.5% Ans.

##### Que-7: Amit Kumar invests Rs36000 in buying Rs100 shares at Rs20 premium. The dividend is 15% per annum. Find : (i) the number of shares he buys   (ii) his yearly dividend   (iii) the percentage return on his investment. Get your answer correct to the nearest whole number.

Solution-  Investment = Rs.36000
Face value = Rs.100
Premium = Rs.20, dividend = 15%
(i) No. of shares
= 36000/120 = 300 Ans.
(ii) Dividend
= 15% of (100 x 300)
= ₹4500 Ans.
(iii) % Return
= (4500/36000) × 100
= 450/36
= 12.5%  = 13% Ans.

##### Que-8: Ajay owns 560 shares of a company. The face value of each shares is Rs25. The company declares a dividend of 9%. Calculate : (i) the dividend that Ajay will get   (ii) the rate of interest on his investment, if Ajay had paid Rs30 for each share.

Solution-  No . of shares = 560
N.V. of one share = ₹ 25
Rate of dividend = 9%
(i)Dividend = No. of shares x N.V. x Rate of dividend.
= 560 x 25 x (9/100)
= ₹ 1,260 Ans.

(ii) Investment = No. of shares x M.V.
= 560 x 30
= ₹ 16,800
∴ Rate of interest on investment = (Dividend/Investment) × 100
= (1,260/16,800) × 100
= 7.5% Ans.

##### Que-9: Mohan Lal invested Rs29040 in 15%, Rs100 shares of a company quoted at a premium of 20%. Calculate : (i) the number of shares bought by Mohan Lal   (ii) his annual income from shares   (iii) the percentage return on his investment

Solution- (i) The cost of each share is Rs.100 plus a premium of 20%, which means he pays 120% of Rs.100 per share.
So, the cost of each share = Rs.100 + (20% of Rs.100) = Rs.100 + Rs.20 = Rs.120
Number of shares:
Number of shares = (29040/120) = 242 Ans.

(ii) The annual income from shares can be calculated using the formula:
Annual income = Number of shares × Face value of each share × Rate of dividend
Annual income = 242×100×0.15 = Rs.3630 Ans.

(iii) Percentage return = (Total investment/Annual income​) × 100
Percentage return = (3630/29040​) × 100
= 12.5% Ans.

##### Que-10: A man invests Rs8800 on buying shares of face value Rs100 each at a premium of 10%. If he earns Rs1200 at the end of the year as dividend, find : (i) the number of shares he has in the company  (ii) the dividend percentage per share

Solution- (i) Total investment = Rs 8,800
Nominal value of 1 share = Rs 100
Market value of 1 share = Rs 110
∴ No of shares purchased = (8800/110)
= 80 Ans.

(ii) Nominal value of 80 shares = 80 × 100 = ₹ 8,000
Let dividend% = y %
then y % of Rs 8,000 = Rs 1,200
⇒ (y/100) × 8000 = 1200
y = 15% Ans.

##### Que-11: A man invests a sum of money in Rs100 shares, paying 10% dividend and quoted at 20% premium. If his annual dividend from these shares is Rs560, calculate : (i) his total investment  (ii) the rate of return on his investment

Solution- Face value of each share = Rs.100
Dividend rate = 10%
Annual dividend = Rs.560
(i) Cost per share = Face value + Premium
Cost per share = 𝑅𝑠.100 + (20%×𝑅𝑠.100)
Cost per share = 𝑅𝑠.100 + 𝑅𝑠.20 = 𝑅𝑠.120
Number of shares = Annual dividend/Dividend per share​
Number of shares = 560/10 = 56
The total investment (T) can be calculated as follows:
T = Number of shares × Cost per share
T = 56×Rs.120 = Rs.6720 Ans.

(ii) The rate of return on investment can be calculated using the formula:
Rate of return = (Annual dividend/Total investment)×100
Rate of return = (560/6720)×100
= (7/84)×100 = 8*(1/3)% Ans.

##### Que-12: A man invests a sum of money in Rs25 shares, paying 12% dividend and quoted at Rs36. If his annual income from these shares is Rs720, calculate : (i) his total investment   (ii) the number of shares bought by him  (iii) the percentage return on his investment

Solution- Dividend per share (D) = 12% of Rs 25 = Rs 3.
Market price per share (Q) = Rs 36.
Annual income from shares = Rs 720.
I = n × D
720 = 𝑛×3
𝑛 = 720/3
n = 240
(i) P = n × Q
P = 240×36
= Rs8640 Ans.

(ii) I = n × D
720 = 𝑛×3
𝑛 = 720/3
n = 240 Ans.

(iii) Percentage return = (720/8640​)×100
= (1/12)​×100 = 8*(1/3)% Ans.

##### Que-13: A man buys 400, Rs10 shares at a premium of Rs2.50 per share. If the rate of dividend is 12%, find : (i) his investment   (ii) annual dividend received by him   (iii) the rate of interest received by him on his money

Solution- Number of shares bought (n) = 400
Face value of each share (F) = Rs 10
Premium per share (P) = Rs 2.50
Rate of dividend (D) = 12%

(i) I = (n×F)+(n×P)
I = (400×10)+(400×2.50)
I = 4000+1000
I = 5000rupees Ans.

(ii) A = n×F×(D/100)
​A = 400×10×(12/100)​
A = 480 rupees Ans.

(iii) Rate of interest = (A/I)​×100
Rate of interest = (5000/480)​×100
Rate of interest = 9.6% Ans.

##### Que-14: Divide Rs35400 into two parts such that if one part is invested in 9%, Rs100 shares at 4% discount and the other in 12%, Rs50 shares at 8% premium, the annual incomes are equal.

Solution-  In First Case,
Investment = Rs.x.
Rate of Dividend = 9%.
Nominal Value of 1 Share(N.V.) = Rs. 100
Market Value of 1 Share(M.V.) = 100 – 100 × 4/100
= Rs. 96
∵ Number of Shares = Sum Invested/M.V. of 1 Share
∴ No. of Shares = x/96
∵ Annual Income = No. of Shares × Rate of Dividend × N.V. of 1 Share.
∴ Annual Income  = (x/96) × (9/100) × 100
⇒ Annual Income = 9x/96
In Second Case,
Investment = Rs. (35400  – x)
N.V. of 1 Share = Rs. 50
M.V. of 1 Share = 50 +  50 × 8/100
= Rs. 54
Rate of Dividend = 12 %
No. of Shares = (35400 – x)/54
Annual Income = (35400 – x)/54 × 12/100 × 50
= Rs. (35400 – x)/9
According to the Question,
Annual Income from both Investments are equals.
∴9x/96 = (35400 – x)/9
1132800 – 32x = 27x
59x = 1132800
⇒ x = Rs. 19200 Ans.
⇒ 35400  – x = Rs. 16200 Ans.

##### Que-15: Divide Rs50760 into two parts such that if one part is invested in 8%, Rs100 shares at 8% discount and the other in 9%. Rs100 shares at 8% premium, the total incomes from both the investments are equal.

Solution- Total investment = Rs 50760
Let 1st part = Rs y
2nd part = Rs (50760 – y)
For 1st part
Nominal value of 1 share = Rs 100
Market value of 1 share = Rs 100 – 8% of Rs 100
= Rs  100- Rs 8 = Rs  92
∴No. shares purchased = y/92 shares
Dividend% = 8%
Dividend on 1 share = 8%  of Rs 100 = Rs 8
Total dividend = (y/92) × Rs 8 = Rs 2y/23
For 2nd part
Nominal value of 1 share = Rs 100
Market value of 1 share = Rs 100 + 8% of  Rs 100
= Rs 100 + Rs 8 = Rs 108
∴ No of shares purchased  = (50760-y)/108 share
Dividend% = 9%
Dividend on 1 share = 9%  of Rs 100 = Rs 9
Total dividend = (50760-y)/108 × Rs 9 = Rs 9(50760-y)/108
Given that both dividend are equal
Then Rs 2y/23 = Rs 9(50760-y)/108
⇒ 2y×108 = 23(456840-9y)
⇒ 216y = (456840 ×23) – 207y
⇒ 423y = 456840×23
⇒ y = (456840×23)/423
= Rs 24840
1 st part = Rs 24840 Ans.
2nd part = Rs 50760- Rs 24840 = Rs 25920 Ans.

##### Que-16: Which is better investment : (10%, Rs100 shares at Rs120) or (8%, Rs100 shares at Rs72)?

Solution- 8%, Rs100 shares at Rs72.
For the first investment:
Initial investment = Rs100 per share
Purchase price = Rs120 per share
Annual return = 10%
So, after one year:
Return per share = Rs120 * 10% = Rs12
Total value per share = Rs120 + Rs12 = Rs132
For the second investment:
Initial investment = Rs100 per share
Purchase price = Rs72 per share
Annual return = 8%
So, after one year:
Return per share = Rs72 * 8% = Rs5.76
Total value per share = Rs72 + Rs5.76 = Rs77.76
Comparing the total value of both investments after one year:
First investment: Rs132 per share
Second investment: Rs77.76 per share
Therefore, the first investment appears to be the better option based on these calculations.

##### Que-17: Which is better investment : (12%, Rs20 shares at Rs16) or (15%, Rs20 shares at Rs24)?

Solution-  let number of shares be x and let x be ₹100
Annual income = no of shares x face value x R/100
In first case
A.I = 100/16 x 20 x 12/100
A.I = ₹15
in second case
A.I = 100/24 x 20 x 15/100
A.I = ₹12.5
therefore the correct answer is (12%, ₹20 shares at ₹16)

##### Que-18: Ashish bought 4500, Rs10 shares paying 12% per annum. He sold them when the price rose to Rs23 and invested the proceeds in Rs25 shares paying 10% per annum, at Rs18. Find the change in his annual income.

Solution-  Number of shares = 4500
Face value of each share = Rs10
Annual return rate = 12%
Annual income = Number of shares * Face value per share * Annual return rate
= 4500 * Rs10 * 12%
= Rs5,400
Selling price per share = Rs23
Total amount = Number of shares * Selling price per share
= 4500 * Rs23
= Rs103,500
Price per share of new shares = Rs18
Annual return rate of new shares = 10%
Number of shares = Total amount received / Price per share
= Rs103,500 / Rs18
= 5750 shares
Annual income = Number of shares * Face value per share * Annual return rate
= 5750 * Rs25 * 10%
= Rs14,375
Change in annual income = Annual income from new shares – Annual income from initial shares
= Rs14,375 – Rs5,400
= Rs8,975 Ans.

##### Que-19: Amit owns 1500, Rs25 shares of a company which declares a dividend of 14%. He sells the shares at Rs40 each and invests the proceeds in 8%, Rs100 shares at Rs80. What is the change in his annual dividend income ?

Solution-  Shares 1500
Share FV = Rs 25
Dividend = 14%
annual Dividend =  number of shares * ( dividend % /100) * FV
= 1500 * (14/100) * 25
= Rs 5250
Shares sold for =  1500 * 40 = Rs 60000
Shares Bought = 60000/80  = 750
Dividend per share = (8/100) 100 = Rs 8
Annual Dividend = 750 * 8  =  Rs 6000
Change in his annual Dividend income = 6000 – 5250  = Rs 750
Rs 750 increase in annual Dividend income

##### Que-20: Vimal sold a certain number of Rs20 shares, paying 8% dividend, at Rs18 and invested the proceeds in Rs10 shares, paying 12% dividend, at 50% premium. If his annual dividend income decreases by Rs120, find the number of shares sold by Vimal.

Solution- Let x be the number of Rs20 shares Vimal sold.
Vimal sold each Rs20 share at Rs18.
Vimal bought Rs10 shares at a 50% premium.
So, the cost of each Rs10 share = Rs10 + (50% of Rs10)
= Rs10 + Rs5 = Rs15.
The number of Rs10 shares Vimal bought = (18x/15) ​= (6x/5)​ shares.
Dividend rate for Rs20 shares = 8%.
Dividend per share for Rs20 shares = Rs20 × 8% = Rs1.60.
Dividend rate for Rs10 shares = 12%.
Dividend per share for Rs10 shares = Rs10 × 12% = Rs1.20.
The number of Rs10 shares Vimal bought = 6x/5​.
So, the annual dividend income from Rs10 shares = 1.20 × (6x/5) = 1.44x rupees.
Annual dividend income from Rs20 shares−Annual dividend income from Rs10 shares = 120 1.60x − 1.44x = 120
0.16𝑥 = 120
𝑥 = 120/0.16
x = 750 Ans.

##### Que-21: A company declares a dividend of 8% on Rs100 shares. Atul buys such shares and gets 10% on his investment. At what price does he buy each share ?

Solution-  Dividend rate = 8%
Face value of each share = Rs100
Atul gets 10% on his investment
So, dividend per share = Rs100 × 8% = Rs8.
Atul gets 10% return on his investment.
So, if he buys each share at price P, his return per share is 0.10P.
Atul’s return per share is equal to the dividend per share:
0.10P = Rs8
Solving for P:
P = Rs8/0.10​
P = Rs80 Ans.

##### Que-22: Deepak invested in Rs25 shares of a company paying 12% dividend. If he received 10% per annum on his investment, at what price did he buy each share ?

Solution- Face value of each share = Rs25
Dividend rate = 12%
Deepak receives 10% per annum on his investment
So, dividend per share = Rs25 × 12% = Rs3.
Deepak receives 10% return on his investment.
So, if he buys each share at price P, his return per share is 0.10P.
Deepak’s return per share is equal to the dividend per share:
0.10P = Rs3
Solving for P:
P = Rs3/0.10​
P = Rs30 Ans.

##### Que-23: At what price should a 10%, Rs25 share be quoted when the money is worth 8% ?

Solution-  Face value of each share = Rs25
Dividend rate = 10%
Interest rate (money worth) = 8%
So, dividend per share = Rs25 × 10% = Rs2.50.
Dividend yield = Dividend per share/Price per share
Solving for :

##### Que-24: How much should a man invest in Rs25 shares, selling at Rs36 to obtain an annual income of Rs1500, if the dividend declared is 12% ?

Solution-  Dividend Rate = 12% = 0.12
Dividend Income = Rs1500
Share Price = Rs36
Face Value of Share = Rs25
Dividend Income per Share = Face Value of Share × Dividend Rate
= Rs25 × 0.12 = Rs3
Now, we need to calculate how many shares can be bought with the investment of x rupees. Since each share costs Rs36, the number of shares bought will be x/36​.
Thus, the total dividend income from all shares will be (𝑥/36) × 3 = x/12​.
We want this to equal Rs1500.
So, we have the equation: x/12 = 1500
Solving for x:
x = 12×1500 = 18000 Ans.

##### Que-25: How much should a man invest in Rs50 shares selling at Rs60 to  obtain an income of Rs450, if the rate of dividend declared is 10%? Also, find his yield percent, to the nearest whole number.

Solution- Dividend Rate = 10% = 0.10
Dividend Income = Rs450
Share Price = Rs60
Face Value of Share = Rs50
Let’s denote the amount to be invested as x.
Dividend Income per Share = Face Value of Share × Dividend Rate
= Rs50 × 0.10 = Rs5
Now, we need to calculate how many shares can be bought with the investment of x rupees. Since each share costs Rs60, the number of shares bought will be x/60​.
Thus, the total dividend income from all shares will be (x/60) × 5 = x/12​.
We want this to equal Rs450.
So, we have the equation:
x/12 = 450
Solving for x:
x = 12×450
= 5400 Ans.
Yield Percent = (Investment Annual/Dividend Income) ​× 100
Given:  Annual Dividend Income = Rs450
Investment = Rs5400
Yield Percent = (5400/450) ​× 100
Yield Percent = (1/12) × 100
Yield Percent = 8.33 = 8% Ans.

##### Que-26: By investing Rs11440 in a company paying 10% dividend, an annual income of Rs520 is received. What is the market value of each Rs50 share?

Solution-  Total investment=11440 rupees
dividend=10%
annual income=520 rupees
nominal value=50 rupees
= suppose he purchased x shares
face value of x shares= 50 x
dividend=50 x *(10/100) = 5 x
then, 5 x = 520
x = 104
market value = total investment/number of shares bought
=    11440/104
= rupees 110 Ans.

##### Que-27: A man invests Rs4500 in shares of a company which is paying 7.5% dividend. If Rs100 shares are available at a discount of 10%, find : (i) number of shares he purchases   (ii) his annual income

Solution-  Rs. 100 shares at a discount of 10%
will cost = 100 – 10
= Rs. 90
(i) ∴ Number of shares = 4500/90
= 50 shares Ans.

(ii) His annual income at 7.5% dividend
Annual income = [Number Of Share × Dividend Percent × 𝐹𝑉]/100
= [50×7.5×100]/100
= 50 × 7.5
Annual income = Rs 375.0 Ans.

##### Que-28: Sachin invests Rs4500 in 10%, Rs100 shares at Rs170. He sells the shares when the price of each share rises by Rs30. He invests the proceeds in 12% Rs100 shares at Rs125. Find : (i) the sale proceeds   (ii) the number of Rs125 shares he buys (iii) the change in his annual income

Solution-  (i) By investing, share bought = 100
By investing, shares bought Rs = (100/170) × 8500 = Rs.5000
Total face value of Rs. 100 shares = Rs. 5000
Income = 10 % of face value
Rs .= (10/100) × 5000 = Rs .500
By selling Rs.100 share, money received = 170 + 30 = Rs. 200
By selling Rs. 5000 shares money, money received Rs = (200/100) × 5000 = Rs.10000
Sale Proceeds = Rs. 10000 Ans.

(ii) By investing Rs. 125, No. of Rs. 100 share bought = 1
By investing Rs. 10000, No. of Rs. 100 shares bought = (10000/125) = 80
∴ No. of Rs. 125 shares bought = 80 Ans.

(iii) By investing Rs. 125 in Rs. 100 share, Income = Rs. 12
By investing Rs. 10000 in Rs. 100 share, Income Rs = (12/125) × 10000 = Rs.960
Increase in income = Rs. 960 – Rs. 500
= Rs. 460 Ans.

##### Que-29: A company with 500 shares of nominal value Rs120 declares an annual dividend of 15%. Calculate : (i) the total amount of dividend paid by the company. (ii) annual income of Mr. Sharma who holds 80 shares of the company. If the return percent of Mr. Sharma from his shares is 10%, find the market value of each share.

Solution- Number of shares = 500
face value or nominal value = 120
Rate of dividend = 15%

(i) Dividend = (15/100) × 500 × 120
= rs 9000 Ans.

(ii) when share is 80
then
dividend = 15% × 80 × 120
= rs 1440 Ans.

(iii) N.V. X D% = Profit% (Return %) X Market Value (M.V.)
120 X (15/100) = (10/100) X M.V.
M.V.= (120 X 100 X 15)/ (100 X 10)
M.V.= Rs. 180 Ans.

— : End of Shares and Dividend Class 10 RS Aggarwal Goyal Brothers Prakashan ICSE Foundation Maths Solutions  : —

Thanks