MATHEMATICS

SALES TAX COMPILED BY SOUVIC JATI 9831497662.

Q. 1. Samir bought a shirt for Rs. 336 including 12% salex tax and necktie for Rs. 110 including 10% sales tax. Find the printed price (without sales tax) of shirt and necktie together.

Q. 2. The price of a T.V. set inclusive of sales tax is Rs.13530. If the rate of sales tax is 10% find its basic price.

Q. 3. Ranjeeta purchases a set of cosmetics and paid Rs. 165 for it including sales tax. If the rate of sales tax is 10%, find the sale price of the set.

Q. 4. A T.V. is available for Rs. 13,440 inclusive of sales tax. If the original cost of T.V. is Rs. 12,000, find the rate of sales tax.

Q. 5. Sunita purchase a bicycle for Rs. 1980. She has paid a sales tax of 10%. Find the list price of the bicycle.

Q. 6. A mini computer is marked for sale for Rs.17,600 which includes sales tax at 10%. Calculate the sales tax.

Q. 7. The printed price of a computer is Rs.24,000. The seller allows a discount of 8% on the printed price. He gives a further off season discount of 5% on the balance. But sales tax at 10% is charged on the remaining amount. Find (i) the sales tax amounts a customer has to pay (ii) the final price he has to pay for computer.

Q. 8. The price of a colour T.V. inclusive of sales tax of 9% is Rs. 13,407. Find its marked price. If the sales tax is increased to 13%, how much more does the customer pay for the T.V.

Q. 9. Kiran purchased an article for Rs. 5,400 which includes 10% rebate on the marked price and 20% sales tax on the remaining price. Find the marked price of the article.

Answers
1. Rs. (300 + 100) = Rs. 400	2. Rs.12,300	3. Rs.150
4. 12%	5. Rs.1800	6. Rs.16000
7. Rs.2097.60 ; Rs.23073.60	8. Rs.12,300 ; Rs.492	9. Rs.5000

Exercise - BANKING

Q. 1. A page from the saving bank account passbook of Mr. Sen is given below. Find the interest Mr. Sen will get from Jan 2006 to June 2006 at the rate of 5% per annum.

Date 2006	Particular	Withdrawals (in Rs.)	Deposits (in Rs.)	Balance (in Rs.)
4 Jan	B/F			1500.00
20 Jan	By cash		1200.00	2700.00
15 Mar	By cheque		2700.00	5400.00
20 Mar	To cheque	1000.00		4400.00
6 June	By cheque		4200.00	8600.00
16 June	To cheque	1200.00		7400.00

Q. 2. A page from Saving Bank Passbook of Mrs. Reva is given below. Calculate the interest received by Mrs. Reva from Jan 2006 to June 2006 at the rate of 5% p.a.

Date 2006	Particular	Withdrawals (in Rs.)	Deposits (in Rs.)	Balance (in Rs.)
1 Jan	By Balance			1500.00
5 Jan	By cash		1200.00	2700.00
20 Jan	By cash		1000.00	3700.00
25 Jan	To cheque	800.00		2900.00
15 Mar	By cash		2500.00	5400.00
20 Mar	To cheque	1000.00		4400.00
6 June	By cash		3000.00	7400.00
25 June	By cash		1200.00	8600.00

Q. 3. A page from the passbook of Kartik is given below. Find the interest he gets from July 2005 to December 2005 at 4% p.a.

Date 2005	Particular	Withdrawals (in Rs.)	Deposits (in Rs.)	Balance (in Rs.)
July - 1	B/F			16000.00
July - 10	By cheque		4000.00	20000.00
Aug - 11	To cheque	16000.00		4000.00
Sept - 19	By cheque		6000.00	10000.00
Nov - 9	By cheque		2000.00	12000.00
Dec - 25	To cheque	8000.00		4000.00

Q. 4. A page from the passbook of Kiran is given below .

Date 2005	Particular	Withdrawals (in Rs.)	Deposits (in Rs.)	Balance (in Rs.)
April - 1	B/F			1500.00
April - 11	By cash		6500.00	8000.00
May - 10	By cheque		6000.00	14000.00
July - 29	To cheque	10000.00		4000.00
August - 11	By cheque		6200.00	10200.00

Kiran closes her account on 5th October, 2005. Find the amount received by kiran if interest is paid at the rate of 4% p.a.

Q. 5. A page from the passbook of Gopal is given below .

Date 2005	Particular	Withdrawals (in Rs.)	Deposits (in Rs.)	Balance (in Rs.)
11- 07 - 05	Deposited		20000.00	20000.00
21 - 07 - 05	To cheque	12000.00		8000.00
19 - 09 - 05	By cheque		4000.00	12000.00
04 - 11 - 05	By cheque		3000.00	15000.00
29 - 12 - 05	To cheque	10000.00		5000.00

Find the interest Gopal gets for the period July 2005 to December 31,2005 at 4% p.a.

Q. 6. A page from the saving bank account is given below :

Date 2005	Particular	Amount withdrawn(in Rs.)	Deposits (in Rs.)	Balance (in Rs.)
01- 07 - 05	B/F			5,000.00
11 - 07 - 05	By cheque		7,000.00	12,000.00
25 - 08 - 05	By cheque			20,000.00
10 - 10 - 05	To cheque	10,000.00	8,000.00	10,000.00
15 - 12 - 05	By cash		12,000.00	22,000.00
29 - 12 - 05	To cheque	19,000.00		3,000.00

The account is closed on 2nd Jan 2006. Find the amount received if the rate of interest is 5% per annum.

Q. 7. A page from the pass book of a savings bank account given below :

Date 2005	Particular	Amount withdrawn(in Rs.)	Deposits (in Rs.)	Balance (in Rs.)
01- 07 - 05	B/F			5000.00
11 - 07 - 05	By cash		7000.00	12,000.00
05 - 09 - 05	By cheque		8,000.00	20,000.00
28 - 10- 05	To cheque	10,000.00		10,000.00
10 - 11- 05	By cash		1,500.00	11,500.00
20 - 11 - 05	To cheque	3,500.00		8,000.00

The account is closed on 10th January 2006. Find the amount received if the rate of interest is 5% per annum.

Answers
1. Rs. 96.25	2. Rs. 102.92 (approx)	3. Rs. 180
4. Rs. 10359	5. Rs. 160	6. Rs. 3250
7. Rs. 8262.50

Exercise – BANKING

Q. 1. Amar opens a recurring deposit account in a bank. He deposits Rs.500 every month for one year. The interest paid by the bank is 5% per annum. Find the amount he receives at the time of maturity.

Q. 2. Shalini opens a recurring deposit account of Rs.100 per month for 5 years. The bank pays 6% as the interest. How much amount will she received after 5 years?

Q. 3. Shankar deposits Rs.300 per month in a recurring deposit account for 12 months. Find the amount he will receive at the time of maturity at the rate of 5% p.a.

Q. 4. Rajani deposits Rs.10000 per month in a recurring deposit account for 6 years at the rate of 6.5% per annum. Find the amount she will get after 6 years at the time of maturity.

Q. 5. Tarique deposits Rs.200 p.m. in a Bank which pays 5.5% interest on recurring deposits. Find the amount he gets at the end of 2 years.

Q. 6. Tarum deposits Rs.450 p.m. in a bank paying 5.5% p.a. recurring deposits. Find the amount due to him after 2 years.

Q. 7. Deepti deposits Rs.400 p.m. in a bank which pays 5.5% simple interest on recurring deposits. Find the amount she gets at the end of 2 years.

Q. 8. Vinod deposits Rs.2500 p.m. in a recurring deposit with a bank paying simple interest at   for 36 months. Find the amount due to him.

Q. 9. Rajaram wants Rs.34575 at the end of 5 years by depositing a certain sum of money on a monthly basis in a bank paying 6% simple interest p.a. What should be the monthly instalment.

Q. 10. Rachna gets Rs.38, 805.75 at the end of 6 years at the rate of 6.5% p.a. in a recurring deposit account. Find the monthly instalment.

Q. 11. Mr. Atul has a cummulative time deposit account in a bank. He deposits Rs.500 per month for a period of 48 months. If at the end of maturity he gets Rs.2940 as the interest, find the rate of interest.

Q. 12. Mrs. Mamun invests Rs.250 every month for 24 months in a bank and collects Rs.6312.50 at the end of the term. Find the rate of simple interest paid by the bank on this recurring deposit.

Q. 13. Which is better investment Rs.40000 in a saving deposit with bank for 3 years the interest being compounded half – yearly at the of 6% or Rs.1200 p.m. in a recurring deposit with a bank paying simple interest at 6% p.a. for 3 years?

Q. 14. Gautam Ghosh deposited Rs.150 per month in State Bank of India for 8 months recurring deposite scheme. What will be the maturity value of the deposit, if the rate of interest is 8% per annum and interest is calculate and at the end of every month.

Answers
1. Rs. 6162.50	2. Rs. 69150	3. Rs. 3697.50
4. Rs. 86235	5. Rs. 5075	6. Rs. 11418.75
7. Rs. 10150	8. Rs. 97631.25	9. Rs. 500
10. Rs. 450	11. 6% p.a.	12. 5% p.a.
13. Former	14. Rs. 1236

Exercise – SHARES AND DIVIDEND

Q. 1. Aruna owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate (i) The dividend Aruna would receive and (ii) The rate of interest, on her investment, considering that she bought these shares @ Rs. 30 per share in the market.

Q. 2. By investing Rs. 7500 in a company paying 10% dividend, an income of Rs. 500 is received. What price is paid for each Rs.100 share?

Q. 3. Mukul invests Rs. 9000 in a company paying a dividend of 6% per annum. When a face value Rs. 100 stands at Rs. 150. What is his annual income? He sells 50% of his shares when the price rises to Rs. 200. What is his gain on this transaction?

Q. 4. A person holds 2,000 shares of a company that have a face value of Rs. 100 each. The company pays a 25% dividend annually. Calculate (i) The annual dividend (ii) The percentage return (Correct to nearest integer) if the shares were bought at a 40% premium.

Q. 5. A company with 10,000 shares of nominal value Rs. 100 declares an annual dividend of 8% to the share holders:

1. Calculate the total amount of dividend paid by the company.
2. Ramesh had bought 90 shares of the company at Rs. 150 per share. Calculate the dividend he receives and the percentage return on his investment.

Q. 6. What sum should a person invest in Rs. 25 shares, selling at Rs. 36, to obtain an income of Rs. 720, if the dividend declared is 12%. Also find (i) the no. of shares bought by the person. (ii) The percentage return on his investment.

Q. 7. A person invested Rs. 8,000 and Rs. 10,000 in buying shares of two companies which later on declared dividends of 12% and 8% respectively. He collects the dividends and sells out all his shares at a loss of 2% and 3% respectively on his investment. Find his total earning from the above transaction.

Q. 8. A man invests a sum of money in Rs.100 shares paying 15% dividend quoted at 20% premium. If his dividend is Rs. 540, Calculate:

1. His total investment
2. The rate of return on his investment.

Q. 9. A lady holds 1,800 ; Rs.100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what percentage return would she get on her investment? Given your answer to the nearest integer.

Q. 10. A company with 10,000 shares of Rs.100 each, declares an annual dividend of 5%;

1. What is the total amount of dividend paid by the company?
2. What would be the annual income of a man, who has 72 shares, in the company?
3. If he received only 4% on his investment, find the price he paid for each share?

Q. 11. Mr. Sharma has 60 shares of nominal value Rs.100 and he decides to sell them when they are at premium of 60%. He invests the proceeds in shares of nominal value of Rs.50, quoted at 4% discount, paying 18% dividend annually. Calculate

1. The sale proceeds.
2. The number of shares he buys
3. His annual dividend from these shares.

Q. 12. A man invests Rs.11,200 in a company paying 6% premium when its Rs.100 shares can be bought for Rs.140. Find

1. His annual dividend
2. Percentage income on his investment.

Q. 13. A man bought 1,000 shares each of face value Rs. 5 at Rs.7 per share. At the end of the year, the company from which he bought the shares declared a dividend of 8%. Calculate

1. The amount of money invested by the man
2. The percentage return on his outlay correct to one decimal place.

Q. 14. A owns 500 shares of Rs. 10 each. Find A’s income, if 14% dividend is declared on these shares in a certain year.

Q. 15. A man bought 360 ten – rupees shares paying 12% premium. He sold them when the price rose to Rs.21 and invested the proceeds in five – rupees shares paying 4.5% per annum at Rs.3.5 per share. Find the annual change in his income.

Q. 16. A person invests Rs.4,368 and buys certain hundred rupee shares at Rs. 91. He sells out shares worth Rs. 2,400 when they have risen to Rs.95 and the remainder when they have fallen to Rs.85. Find the gain or loss on the total transaction.

Q. 17. A man invests Rs. 2,688 in buying shares of nominal values Rs. 24 and selling at 12% premium. The dividend on the shares is 15% per annum.

1. Calculate the number of shares he buys
2. Calculate the dividend he receives annually.

Answers
1. (i) Rs. 1260 (ii) 7.5%	2. Rs. 150	3. Rs. 360 ; Rs. 1500
4. (i) Rs. 50,000 (ii) 18%	5. (i) Rs. 80,000 (ii) Rs. 720 ; 5(1/3%)	6. Rs. 8,640 (i) 240 (ii) 8(1/3%)
7. Rs. 1,300.	8. (i) Rs. 4,320 (ii) 12.5%	9. Rs. 27,000 ; 11%
10. (i) Rs. 50,000 (ii) Rs. 360 (iii) Rs. 125.	11. (i) Rs. 9,600 (ii) Rs. 200 (iii) Rs. 1,800	12. (i) Rs. 480 (ii) 4(2/7)%
13. (i) Rs. 7,000 (ii) 5.7%	14. (i) Rs. 700	15. (i) Gain Rs. 54
16. Loss Rs. 48	17. (i) Rs. 100 (ii) Rs. 360

Exercise –FACTOR THEPREM   BY SOUVIC JATI  9831497662

Q. 1. Determine the value of ‘a’ such that (x - 4) is a factor of 2x³ + ax² + 27x - 28.

Q. 2. Show that 2x - 7 is a factor of 2x³ + x² - 22x - 21. Hence factorise the given expression completely, using factor theorem.

Q. 3. Show that 3x + 5 is factor of 3x³ - 16x² - 5x + 50. Hence factorise the given expression completely using factor theorem.

Q. 4. Find the value of k so that (x - 1) is a factor of k²x - 2kx - 3.

Q. 5. Find the value of k so that (x - 3) is a factor of polynomial k²x² - kx - 2.

Q. 6. Find the value of k so that (x + 1) is a factor of k²x² - 2kx - 3.

Q. 7. If (x - 4) is a factor of x³ + ax² + 2bx - 24 and a - b = 8, find the value of a and b.

Q. 8. If (x + 3) is a factor of x³ + ax² - bx + 6 and a + b = 7, find the value of a and b.

Q. 9. If (x + 2) is a factor of x³ + ax² + 4bx + 12 and a + b = -4, find the value of a and b.

Q. 10. Find the value of a and b so that the polynomial x³ + ax² + bx - 6 has a factor x² - 4x +3.

Q. 11. Find the value of a and b so that the polynomial x³ + ax² + bx + 15 is divisible by x² + 2x - 15.

Answers OF FACTOR THEOREM
1. -13	2. Yes, (2x - 7) (x + 1) (x + 3)	3. Yes, (3x + 5) (x - 2) (x - 5)
4. 3, -1	5. 2/3, -(1/3)	6. -3, 1
7. a = 1, b = -7	8. a = 0, b = 7	9. a = -3, b = -1
10. a = -6, b = 11	11. a = 1, b = -17