In ICSE Class 10 Mathematics, the topic of shares and dividends holds significant importance. Understanding this concept is very important for students as it involves practical applications of mathematical calculations in real-life scenarios. In this article, we will do Shares And Dividends PYQs Solution for ICSE Class 10 Mathematics. We will cover all the questions that have appeared in ICSE examinations from the year 2010 till last year and provide detailed step-by-step solutions. So, let’s start solving shares and dividends PYQs (previous years’ questions) and be more confident to score well in Board examination.
Download ICSE Class 10 Maths Shares And Dividends PYQs Solution PDF
ICSE Class 10 Maths Shares And Dividends PYQs Solution
1. A company with 500 shares of nominal value ₹ 120 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. [2020]
Solution: (i) ₹ 9000 (ii) Annual income= ₹1440; M.V.= ₹180
Step-by-step Explanation:
\[\style{font-size:14px}{No.\;of\;shares\;=\;500\\Face\;value\;(f)\;=\;₹\;120\\Rate\;of\;dividend\;=\;15\%\\\\(i)\;Total\;dividend=\frac{n\times r\times f}{100}\\\;\;\;\;=\frac{500\times15\times120}{100}\\\;\;\;=₹9000\\\\(ii)\;Annual\;income\;of\;Mr.\;Sharma\\\;=\frac{n\times r\times f}{100}\\\;\;\;\;\;\;\;=\frac{80\times15\times120}{100}\\\;\;\;\;\;\;=₹1440\\Return\;\%\;of\;Mr.\;Sharma=\;10\%\\We\;know,\;return\%\;=\;\frac{income}{investment}\times100\\\Rightarrow10=\frac{1440}{80\times M.V.}\times100\\\Rightarrow10=\frac{1800}{M.V.}\\\Rightarrow10\times M.V.=1800\\\Rightarrow M.V.=\;180\\Hence,\;M.V.\;=\;₹180}\]
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2. A man invests 4500 in shares of a company which is paying 7.5% dividend. If 100 shares are available at a discount of 10%. Find:
(i) Number of shares he purchases.
(ii) His annual income. [2019]
Solution: (i) 50 (ii) ₹ 375
Step-by-step Explanation:
\[\style{font-size:14px}{Investment=₹4500\\Face\;value\;(f)\;=\;₹100\\Market\;Value\;(M.V.)\\=₹100-10\%\;of\;100\\\;=₹\;90\\Rate\;of\;dividend\;=\;7.5\%\\\\(i)\;Number\;of\;shares=\;\frac{Investment}{M.V.}\\\;\;\;\;\;\;\;\;\;\;\;\;\;=\frac{4500}{90}\\\;\;\;\;\;\;\;\;\;\;\;\;=50\;shares\\\\(ii)\;His\;annual\;income=\frac{n\times r\times f}{100}\\\;\;\;\;=\frac{50\times7.5\times100}{100}\\\;\;\;=₹375\\}\]
3. Sachin invests ₹ 8500 in 10%, ₹ 100 shares at ₹ 170. He sells the shares when the price of each share rises by ₹ 30 He invests the proceeds in 12% ₹ 100 shares at ₹ 125. Find:
(i) the sale proceeds.
(ii) the number of ₹ 125 shares he buys.
(iii) the change in his annual income. [4] [2019]
Solution: (i) 10,000 (ii) 80 (iii) ₹460 (increase)
Step-by-step Explanation:
\[\style{font-size:14px}{1st\;Investment=₹8500\\Face\;value\;(f)\;=\;₹100\\Market\;Value\;(M.V.)=₹170\\Rate\;of\;dividend\;=\;10\%\\M.V.\;at\;the\;time\;of\;sale\\=₹170+30=₹200\\Hence,\;no.\;of\;shares\;purchased\;earlier\\=\;\frac{investment}{M.V.}\\\;\;\;\;\;=\frac{8500}{170}=\;50\\(i)\;The\;sale\;proceeds\\=\;no.\;of\;shares\times M.V.\;at\;the\;time\;of\;sale\\\;\;\;\;\;\;=50\times200\\\;\;\;\;\;\;=₹10000\\Now,\;2nd\;investment=\;₹10000\\r\%=\;12\%\\f=\;₹100\\M.V.=\;₹125\\(ii)\;Number\;of\;₹125\;shares\;he\;buys\\=\;\frac{Investment}{M.V.}\\\;\;\;\;\;\;\;\;\;\;\;\;\;=\frac{10000}{125}\\\;\;\;\;\;\;\;\;\;\;\;\;=80\\(iii)\;His\;annual\;income\;earlier\\=\frac{n\times r\times f}{100}\\\;\;\;\;=\frac{50\times10\times100}{100}\\\;\;\;=₹500\\His\;annual\;income\;later\\=\;\frac{80\times12\times100}{100}\\\;\;\;\;=₹960\\Hence,\;change\;in\;annual\;income\\=\;₹(960-500)\\\;=₹460\;(increase)\\}\]
4. A man invests ₹ 22,500 in ₹ 50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate: [3]
(i) The number of shares purchased.
(ii) The annual dividend received.
(iii) The rate of return he gets on his investment. Give your answer correct to the nearest whole number. [2018]
Solution: (i) 500 (ii) ₹ 3000 (iii) 13 1/3%
Step-by-step Explanation:
\[\style{font-size:14px}{Investment=₹22500\\Face\;value\;(f)\;=\;₹50\\Market\;Value\;(M.V.)=₹50-10\%of\;50\\\;\;\;\;\;\;\;=50-5=\;₹45\\Rate\;of\;dividend\;=\;12\%\\(i)\;The\;no.\;of\;shares\;purchased\\=\;\frac{investment}{M.V.}\\\;\;\;\;\;=\frac{22500}{45}=\;500\\(ii)The\;annual\;dividend\\=\frac{n\times r\times f}{100}\\\;\;\;\;=\frac{500\times12\times50}{100}\\\;\;\;=₹3000\\(iii)\;Rate\;of\;return\;on\;investment\\=\;\frac{income}{investment}\times100\\\;\;\;\;\;=\frac{3000}{22500}\times100\\\;\;\;\;=\frac{40}3\%\\\;=\;13\frac13\%\\}\]
5. How much should a man invest in ₹50 shares selling at ₹60 to obtain an income of 450, if the rate of dividend declared is 10%. Also, find his yield percent, to the nearest whole number. [3] [2017]
Solution: Investment= ₹5400 ; Yield= 8%
Step-by-step Explanation:
\[\style{font-size:14px}{N.V.=\;₹50\\M.V.=\;₹60\\Income=\;₹450\\rate\;of\;dividend\;(r)=10\%\\\\Dividend\;on\;1\;share\\=10\%\;of\;₹50\\=\frac{10}{100}\times50\\=₹5\\\\No.\;of\;shares=\frac{Total\;dividend}{dividend\;on\;1\;share}\\\;\;\;=\frac{450}5=90\\\therefore Investment=n\times M.V.\\\;\;\;\;=90\times60\\\;\;\;=₹5400\\\\Yield\%=\frac{Income}{Investment}\times100\\\;\;\;\;=\frac{450}{5400}\times100\\\;\;\;\;=8.33=\;8\%}\]
6. Ashok invested ₹26,400 on 12%, ₹25 shares of a company. If he receives a dividend of ₹2,475, find the:
(i) number of shares he bought.
(ii) Market value of each share. [3] [2016]
Solution: (i) 825 (ii) ₹32
Step-by-step Explanation:
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ICSE Class 10 Maths Previous Years Questions Solution Chapter-wise
7. Rohit invested ₹9,600 Rs.100 shares at ₹20 premium paying 8% dividend. Rohit sold the shares when the price rose to ₹160. He invested the proceeds (excluding dividend) in 10% ₹50 shares at ₹40. Find the:
i. original number of shares.
ii. sale proceeds.
iii. new number of shares.
iv. change in the two dividends. [4] [2015]
Solution: (i) 80 (ii) ₹12800 (iii) 320 (iv) ₹960
Step-by-step Explanation:
\[\style{font-size:14px}{Investment=₹9600\\N.V.=₹100\\M.V.=100+20=₹120\\rate\;of\;dividend=8\%\\\\(i)\;original\;no.\;of\;shares\\=\frac{Investment}{M.V.}\\=\frac{9600}{120}\\=80\\\\(ii)\;He\;sold\;the\;shares\;at\;M.V.\;₹160\\Sale\;proceeds=160\times80\\=₹12800\\\\New\;investment=₹12800\\N.V.=₹50\\M.V.=₹40\\rate\;of\;dividend=10\%\\(iii)\;New\;number\;of\;shares\\=\frac{Investment}{M.V.}\\=\frac{12800}{40}\\=320\\(iv)\;Earlier\;dividend\\=\frac{n\times r\times f}{100}\\=\frac{80\times\times8\times100}{100}\\=₹640\\New\;dividend\\=\frac{320\times10\times50}{100}\\=₹1600\\Hence,\;change\;in\;dividend\\=₹1600-₹640\\=₹960\;(increase)}\]
8. Salman invests a sum of money in ₹ 50 shares, paying 15% dividend quoted at 20% premium. If his annual dividend is ₹ 600, calculate:
(i) the number of shares he bought.
(ii) his total investment.
(iii) the rate of return on his investment. [3] [2014]
Solution: (i) 80 (ii) ₹ 4800 (iii) 12.5%
Step-by-step Explanation:
\[\style{font-size:14px}{N.V.=₹50\\M.V.=50+20\%\;of\;50=₹60\\rate\;of\;dividend=15\%\\Annual\;dividend=₹600\\\\Dividend\;on\;1\;share\\=15\%\;of\;₹50\\=₹7.50\\\\(i)\;So,\;no.\;of\;shares\\=\frac{Total\;dividend}{dividend\;on\;1\;share}\\=\frac{600}{7.50}\\=80\\\\(ii)\;Total\;investment\\=n\times M.V.\\=80\times60\\=₹4800\\\\(iii)\;rate\;of\;return\;on\;investment\\=\frac{Income}{Investment}\times100\\=\frac{600}{4800}\times100\\=\frac{25}2\%\\=12.5\%}\]
9. Salman buys 50 shares of face value ₹100 available at ₹132.
(i) What is his investment?
(ii) If the dividend is 7.5%, what will be his annual income?
(iii) If he wants to increase his annual income by ₹150, how many extra shares should he buy? [4] [2013]
Solution: (i) ₹ 6600 (ii) ₹ 375 (iii) 20
Step-by-step Explanation:
\[no.\;of\;shares=\;50\\face\;value\;(f)=\;₹100\\M.V.=\;₹132\\dividend\%=\;7.5\%\\(i)\;Investment=\;n\times M.V.\\\;\;\;=50\times132\\\;\;\;=₹6600\\\\(ii)\;Annual\;income\\\frac{n\times r\times f}{100}\\=\frac{50\times7.5\times100}{100}\\=₹375\\\\(iii)\;Dividend\;on\;1\;share\\=7.5\%\;of\;₹100\\=₹7.50\\If\;he\;wants\;to\;increase\;annual\;income\;by\;₹150\\No.\;of\;extra\;shares\\=\frac{increase\;in\;annual\;income}{income\;on\;1\;share}\\\;\;=\frac{150}{7.50}\\\;\;=20\]
10. A man invests ₹9,600 on ₹100 shares at ₹80. If the company pays him 18% dividend find:
(i) the number of shares he buys.
(ii) his total dividend.
(iii) his percentage return on the shares [3] [2012]
Solution: (i) 120 (ii) ₹ 2160 (iii) 22.5%
Step-by-step Explanation:
\[Investment=\;₹9600\\face\;value\;(f)=\;₹100\\M.V.=\;₹80\\dividend\%=\;18\%\\(i)\;No.\;of\;shares=\;\frac{investment}{M.V.}\\\;\;\;=\frac{9600}{80}\\\;\;\;=120\\\\(ii)\;Total\;dividend\\=\frac{n\times r\times f}{100}\\=\frac{120\times18\times100}{100}\\=₹2160\\\\(iii)\;percentage\;return\;on\;share\\=\frac{income}{investment}\times100\\=\frac{2160}{9600}\times100\\=22.5\%\]
11. Mr. Parekh invested ₹ 52,000 on ₹100 shares at a discount of ₹ 20 paying 8% dividend. At the end of one year he sells the shares at a premium of ₹ 20. Find
(i) The annual dividend.
(ii) The profit earned including his dividend. [3] [2011]
Solution: (i) ₹ 5200 (ii) ₹ 31200
Step-by-step Explanation:
\[Investment=\;₹52000\\face\;value\;(f)=\;₹100\\M.V.=\;100-20=₹80\\dividend\%=\;8\%\\Hence,\;no.\;of\;shares=\\\frac{investment}{M.V.}\\=\frac{52000}{80}\\=650\\(i)\;Annual\;dividend\\=\frac{n\times r\times f}{100}\\=\frac{650\times8\times100}{100}\\=₹5200\\He\;sold\;shares\;at(100+20)=₹120\\(ii)\;Hence,\;sale\;proceeds\\=650\times120\\=₹78000\\Therefore,\;profit=\;78000-52000\\\;\;=₹26000\\Hence,\;profit\;earned\;including\;dividend\\=₹26000+₹5200\\=₹31200\]
12. Vivek invests ₹ 4,500 in 8%, ₹ 10 shares at ₹ 15. He sells the shares when the price rises to ₹ 30, and invests the proceeds in 12% ₹ 100 shares at ₹ 125. Calculate:
(i) the sale proceeds.
(ii) the number of ₹125 shares he buys.
(iii) the change in his annual income from dividend. [4] [2010]
Solution: (i) ₹9000 (ii) 72 (iii) ₹ 624
Step-by-step Explanation:
\[Investment=\;₹\;4500\\Rate\;of\;dividend=\;8\%\\face\;value=\;₹\;10\\M.V.=\;₹15\\No.\;of\;shares=\frac{investment}{M.V.}\\\;=\frac{4500}{15}\\\;=300\\His\;annual\;income\\=\frac{n\times r\times f}{100}\\=\frac{300\times8\times10}{100}\\=₹240\\When\;price\;rises\;to\;₹30,\\he\;invests\;the\;shares.\\(i)\;Hence,\;sale\;proceeds\\=300\times30\\=₹9000\\His\;next\;investment\\Investment=\;₹9000\\rate\;of\;dividend=\;12\%\\face\;value=\;₹100\\M.V.\;=\;₹125\\No.\;of\;shares\;purchased\\=\frac{9000}{125}\\=72\\(iii)\;Now\;his\;annual\;income\\=\frac{n\times r\times f}{100}\\=\frac{72\times12\times100}{100}\\=₹864\\Therefore,\;change\;in\;his\;annual\;income\\=₹864-₹240\\=₹624\;(increase)\\\]
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