#### Chapters

## Chapter 9: Commercial Mathematics

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 9 Commercial Mathematics Exercise 9.1 [Page 124]

Find 77% of 580 + 34% of 390.

240 candidates appeared for an examination, of which 204 passed. What is the pass percentage?

What percent of 8.4 kg are 168 grams?

If the length of a rectangle is decreased by 20%, what should be the increase in the breadth of the rectangle so that the area remains the same?

The price of rice increased by 20%, as a result, a person can have 5 kg of rice for ₹ 600. What was the initial price of rice per kg?

What percent is 3% of 5%?

After availing two successive discounts of 20% each, Madhavi paid Rs 64 for a book. If she would have got only one discount of 20%, how much additional amount would she have paid?

The price of the table is 40% more than the price of a chair. By what percent price of a chair is less than the price of a table?

A batsman scored 92 runs which included 4 boundaries 5 sixes. He scored other runs buy running between the wickets. What percent of his total score did he make by running between the wickets?

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 9 Commercial Mathematics Exercise 9.2 [Page 127]

Mr. Sarad purchased a laptop for Rs. 24000 and sold it for Rs. 30000. What was the profit percentage?

Shraddha purchases a mobile phone and refrigerator for Rs. 18000 and 15,000 respectively. She sold the refrigerator at a loss of 20% and the mobile at a profit of 20%. What is her overall profit or loss?

A vendor bought toffees at 6 for Rs.10. How many for Rs.10 must he sell to gain 20%?

The percentage profit earned by selling an article for Rs. 2880 is equal to the percentage loss incurred by selling the same article for Rs. 1920. At what price the article should be sold to earn a 25% profit?

A cloth merchant advertises selling cloth at a 4% loss. By using a faulty meter scale, he is earning a profit of 20%. What is the actual length of the scale?

Sunil sells his bike worth Rs. 25000 to Rohit at a profit of 20%. After 6 months Rohit sells the bike back to Sunil at a loss of 20%. Find the total profit percent of Sunil considering both the transactions.

By selling a book at Rs. 405 bookseller incurs a loss of 25%. Find the cost price of the book.

A cloth costs Rs. 675. If it is sold at a loss of 20%, what is its cost price as a percentage of its selling price?

Ashwin buys an article for Rs. 500. He marks it for sale at 75% more than the cost price. He offers a 25% discount on the marked price to his customer. Calculate the actual percentage of profit made by Ashwin.

The combined cost price of a refrigerator and a mixture is Rs. 12400. If the refrigerator costs 600% more than the mixer, find the cost price of the mixture.

Find the single discount equivalent to the discount series of 5%, 7%, and 9%.

The printed price of a shirt is Rs. 390. Lokesh pays Rs. 175.50 for it after getting two successive discounts. If the first discount is 10%, find the second discount.

Amar, a manufacturer, gives a discount of Rs. 25% on the list price to his distributor Akbar, Akbar sales at a 10% discount on the list price to his customer Anthony. Anthony paid Rs 540 for the article. What is the profit percentage of Akbar on his cost price?

A man sells an article at a profit of 25%. If he had bought it at 10% less and sold it for Rs 7 less, he would have gained 35%. Find the cost price of the article.

Mr. Mehta sold his two luxury cars at Rs. 39,10,000 each. On one he gains 15% but on the other, he loses 15%. How much does he gain or lose in the whole transaction?

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 9 Commercial Mathematics Exercise 9.3 [Page 130]

What would be the simple interest on an amount of Rs. 9600 at the rate of 6% per annum after 3 years?

What would be the simple interest at the rate of `9 1/2%` per annum on Rs. 6000 for `2 1/2` years?

What would be the simple interest on Rs. 8400 in 9 months at the rate of 8.25 percent per annum?

What would be the compound interest on Rs 4200 for 18 months at 10% per annum compounded half-yearly?

Find the compound interest on Rs.10000 for 2 years at 8% per annum compounded half-yearly.

In how many years Rs. 1,00,000 will become Rs. 1,33,100 at a compound interest rate of 10% per annum?

A certain sum of money becomes three times itself in 20 years at simple interest. In how many years does it become double of itself at the same rate of simple interest?

A person borrows 10000 for 2 years at 4% p a simple interest he immediately lends it to another person at 6.5 % p. a. for 2 years. Find his total gain in the transaction.

A man deposits Rs 200 at the end of each year in a recurring account at 5% compound interest. How much will it become at the end of 3 years?

A man gets a simple interest of Rs. 2,000 on a certain principal at the rate of 5% p.a. in 4 years. What compound interest will the man get on twice the principal in 2 years at the same rate?

The difference between simple interest and compound interest on a certain sum of money is Rs.32 at 8% per annum for 2 years. Find the amount.

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 9 Commercial Mathematics Exercise 9.4 [Page 132]

Kanchan purchased a Maruti car for Rs.2,45,000/- and the rate of depreciation is `14 2/7 %` per annum. Find the value of the car after two years?

The value of a machine depreciates from Rs.32768 to Rs.21,952/- in three years. What is the rate of depreciation?

The value of a machine depreciates at a rate of 10% every year. It was purchased 3 years ago. Its present value is Rs.2,18,700/-. What was the purchase price of the machine?

Mr. Manish purchased a motorcycle at Rs.70,000/-. After some years he sold his motorcycle at the exact depreciated value of it that is Rs.51,030/-. The rate of depreciation was taken as 10%. Find after how many years he sold his motorcycle.

Mr. Chetan purchased furniture for her home at Rs.5,12,000/-. Considering the rate of depreciation as 12.5%, what will be the value of furniture after 3 years.

Grace Fashion Boutique purchased a sewing machine at Rs.25,000/-. After 3 years machine was sold at a depreciated value Rs.18,225/- Find the rate of depreciation.

Mr. Pritesh reduced the value of his assets by 5% each year, which were purchased for Rs.50,00,000/-. Find the value of assets after 2 years.

A manufacturing company is allowed to charge a 10% depreciation on its stock. The initial value of the stock was Rs.60,000/-. After how many years the value of the stock will be 39366?

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 9 Commercial Mathematics Exercise 9.5 [Pages 133 - 134]

Three partners shared the profit in a business in the ratio 5 : 6 :7 . They had partnered for 12 months, 10 months, and 8 months respectively. What was the ratio of their investments?

Kamala, Vimala, and Pramila enter into a partnership. They invest in Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, Vimala withdraws Rs. 40,000, while at the end of the second year, Pramila withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?

Sanjeev started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Sanjeev invested another additional amount of Rs.10,000 and Pawan joined them with an amount of Rs.35,000. What will be Rajeev’s share in the profit of Rs.1,50,000 earned at the end of 3 years from the start of the business in 1999?

Teena, Leena, and Meena invest in a partnership in the ratio: 7/2,4/3,6/5. After 4 months, Teena increases her share by 50%. If the total profit at the end of one year is Rs.21,600, then what is Leena’s share in the profit?

Dilip and Pradeep invested amounts in the ratio 2:1, whereas the ratio between amounts invested by Dilip and Sudip was 3:2. If Rs. 1,49,500 was their profit, how much amount did Sudip receive?

The ratio of investments of two partners Jatin and Lalit is 11:12 and the ratio of their profits is 2 : 3. If Jatin invested the money for 8 months, find for how much time Lalit invested his money.

Three friends had dinner at a restaurant `2/3` When the bill was received, Alpana paid as much as Beena paid and Beena paid `1/2` as much as Catherin paid. What fraction of the bill did Beena pay?

Roy starts a business with Rs. 10000, Shikha joins him after 2 months with 20% more investment than Roy, after 2 months Tariq joins him with 40% less than Shikha. If the profit earned by them at the end of the year is equal to twice the difference between the investment of Roy and ten times the investment of Tariq. Find the profit of Roy?

If 4 (P’s Capital) = 6(Q’s Capital) = 10(R’s Capital), then out of the total profit of Rs 5580, what is R’s share?

A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest at the rate of 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 9 Commercial Mathematics Exercise 9.6 [Pages 138 - 139]

M/s Janaseva sweet mart sold sweets of Rs.3,86,000. What CGST and SGST he will pay if the rate of GST is 5%?

Janhavi Gas Agency purchased some gas cylinders for Rs. 500000 and sold them to the customers for Rs. 590000. Find the amount of GST payable and the amount of ITC 5% GST is applicable.

A company dealing in mobile phones purchased mobile phones worth Rs500000 and sold the same to customers at Rs.6,00,000. Find the amount Of ITC and the amount of GST if the rate of GST is 12%.

Prepare Business to customers (B2C) tax invoice using the given information. Write the name of the supplier, address, state, Date, Invoice Number, GSTIN, etc. as per your choice

Supplier: M/s _________________ Address: _________________ State: ________________ Date: _________________ Invoice No: ______________ GSTIN: ___________________

Particular: Rate of Sarees – Rs.2750 Rate of GST 5% HSN 5407–2 pcs

Rate of Kurta – Rs. 750 Rate of GST 12% HSN 5408.

Heena Enterprise sold cosmetics worth Rs. 25000 to Leena traders, a retailer. Leena Traders sold it further to Meena Beauty Products for Rs. 30000. Meena Beauty Product sold it further to the customers for Rs. 40000. The rate of GST is 18%

Find

i) GST Payable by each party

ii) CGST and SGST

‘Chitra furnishings’ purchased tapestry (curtain cloth) for Rs. 2800000 and sold for Rs.4480000 Rate of GST is 5%.

Find,

i) Input Tax

ii) Output Tax

iii) ITC

iv) CGST and SGST

Two friends ‘Aditi’ and ‘Vaishali’ went to a restaurant. They ordered 2 Masala Dosa costing Rs. 90 each 2 coffee costing Rs.60 each and 1 sandwich costing Rs. 80. If GST is charged at 5% Find the Total amount of the bill including GST.

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 9 Commercial Mathematics Exercise 9.7 [Pages 141 - 142]

Shantanu has a choice to invest in Rs.10 shares of two firms at Rs.13 or at Rs.16. If the first firm pays a 5% dividend and the second firm pays a 6% dividend per annum,

** find: **

**(i) **Which firm is paying better?

** (ii) **If Shantanu invests equally in both the firms and the difference between the return from them is Rs. 30. Find how much, in all, does he invest.

A dividend of 9% was declared on Rs.100 shares selling at a certain price in the stock market. If the rate of return is 7.5%, calculate

(i) The market price of each share, and

(ii) The amount to be invested to obtain an annual dividend of Rs. 630.

Nilesh has the option of investing his money in 8% Rs. 10 shares at a premium of Rs.3.50 or 7% Rs. 100 shares at a premium of 20%. Which of the two investments will be more profitable for him?

Sudhakar invests Rs. 1344 in buying shares of face value Rs.24 selling at 12% premium. The dividend on the shares is 15% per annum. Calculate

(i) The number of shares Sudhakar buys, and

(ii) The dividend he receives annually.

Sameer invests Rs. 5625 in a company paying 7% per annum when the share of Rs. 10 stands for Rs.12.50. Find Sameer’s income from this investment. If he sells 60 % of these shares for Rs.10 each, find his gain or loss in this transaction.

Geeta buys Rs.100 shares of a company that pays a 15 % dividend. She buys the shares at a price from the market that gives her a 10% return on her investment. At what price did she buy each share?

Tejas invests in 9% Rs. 100 shares at Rs. 145 but Shail invests in 7% Rs. 100 shares at Rs.116. whose investment is better?

A 6% share yields 8%. Find the market value of a Rs 100 share.

Ashwini bought Rs. 40 shares at a premium of 40%. Find the income, if Ashwini invests Rs. 14000 in these shares and receives a dividend at the rate of 8% on the nominal value of the shares.

Mr. Rutvik Invests Rs. 30,000 in buying shares of a company that pays a 12 % dividend annually on Rs. 100 shares selling at a premium of Rs. 50. Find

(i) The number of shares bought by Mr. Rutvik, and

(ii) His annual income from the shares.

Rasika bought Rs. 40 shares at a discount of 40%. Find the income, if she invests Rs.12000 in these shares and receives a dividend at the rate of 11% on the nominal value of the shares.

Nisha invests Rs. 15840 in buying shares of nominal value Rs.24 selling at a premium of 10%. The company pays a 15% dividend annually.

Find

(i) The dividend she receives annually, and

(ii) The rate of return from her investment.

Ashutosh buys 400, Rs. 100 shares at a discount of 20 % and receives a return of 12% on his money. Calculate:

(i) The amount invested by Ashutosh.

(ii) The rate of dividend paid by the company.

Vaishnavi bought 1000, Rs.100 shares from the stock market carrying an 8% dividend quoted at Rs.130. A few days later the market value of the shares went up by 10%. Vaishnavi sold all her shares. What was her total income from this transaction?

Mr. Dinesh invests Rs. 20800 in 6% Rs. 100 shares at Rs. 104, and Rs. 14300 in 10.5% Rs. 100 shares at Rs.143. What will be his annual income from the shares?

A company declares a semi-annual dividend of 5%. Daniel has 400 shares of the company. If Daniel’s annual income from the shares is Rs. 1000, find the face value of each share.

Bhargav buys 400, twenty-dollar shares at a premium of Rs. 4 each and receives a dividend of 12%.

Find:

(i) The amount invested by Bhargav

(ii) His total income from the shares.

(iii) Percentage return on his money.

Anil buys 350 Rs 100 shares of a company at a premium of 20% from the market. The company pays a 12% dividend annually.

Find

(i) the investment made by the Anil,

(ii) his annual income from the shares, and

(iii) the rate of return from the shares.

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 9 Commercial Mathematics Miscellaneous Exercise 9 [Pages 143 - 144]

A man buys a house for Rs 10 lakh and rents it. He puts 10% of the annual rent aside for repairs, Pays Rs. 1000 as annual taxes and realizes 8% on his investment thereafter. Find the annual rent of the house.

Rose got 30% of the maximum marks in an examination and failed by 10 marks. However, Lily who appeared for the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?

Ankita's Salary was reduced by 50%. Again the reduced salary was increased by 50%. Find loss in terms of percentage.

By selling 300 lunch boxes, a shopkeeper gains the selling price of 100 lunch boxes. Find his gain percentage.

A salesman sold an article at a loss of 10%. If the selling price has been increased by Rs. 80, there would have been a gain of 10%. What was the cost of the article?

Find the single discount equivalent to a series discount of 10%, 20%, and 15%.

Reshma put an amount at simple interest at a certain rate for 3 years. Had she been put at a 2% higher rate, she would have received Rs 360 more. Find the sum.

The compound interest on Rs. 30000 at 7% p.a. is Rs. 4347. What is the period in years?

The value of the machine depreciates at the rate of 15% p.a. It was purchased 2 years ago. Its present value is Rs. 7225. What was the purchase price of the machine?

A tree increases annually by 1/8 of its height. By how much will it increase after 2½ years. If its length today is 8 m.?

A building worth Rs. 121000 is constructed on land worth Rs. 81000. After how many years will the value of both be the same if land appreciates at 10% pa. and buildings depreciate at 10% p.a.

Varun invested 25%, 30%, and 20% of his savings in buying shares of three different companies. ‘A’, ‘B’ and ‘C’ which declared dividends. 10%, 12% and 15% respectively. If his total income on account of dividends is Rs. 6370/-, find the amount he invested in buying shares of company ‘B’.

Find the annual dividend received from Rs. 25000, 8% stock at 108.

A, B, and C enter into a partnership. A invests 3 times as much as B invests and B invests two-thirds of what ‘C’ invests. At the end of the year, the profit earned is Rs. 8800. What is the share of ‘B’?

The ratio of investment of two partners Santa and Banta is 11 : 12 and the ratio of their profits is 2 : 3. If Santa invested the money for 8 months, then for how much time Banta his money?

Akash, Sameer, and Sid took a house on rent for once a year for Rs.16236. They stayed together for 4 months and then sid left the house. After 5 more months. Sameer also left the house. How much rent should each pay?

Ashwin Auto Automobiles sold 10 motorcycles. The total sales amount was Rs. 680000. 18% of GST is applicable. Calculate how much CGST and SGST the firm has to pay.

‘Sweet 16’ A ready-made garments shop for Women's garments, purchased stock for Rs. 400000 and sold that stock for 550000 ( 12% GST is applicable)

Find,

i) Input Tax Credit

ii) CGST and SGST paid by the firm.

## Chapter 9: Commercial Mathematics

## Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 9 - Commercial Mathematics

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Concepts covered in Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 9 Commercial Mathematics are Percentage, Profit and Loss, Simple and Compound Interest, Depreciation, Partnership, Goods and Service Tax (GST), Shares and Dividends.

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