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A man deposited Rs 10000 in a bank at th...

A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in `15^(th)` year since he deposited the amount and also calculate the total amount after 20 years.

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The correct Answer is:
Rs 17000; 20,000
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Consider a tank which initially holds V_(0) liter of brine that contains a lb of salt. Another brine solution, containing b lb of salt per liter is poured into the tank at the rate of eL//"min" . The problem is to find the amount of salt in the tank at any time t. Let Q denote the amount of salt in the tank at any time. The time rate of change of Q, (dQ)/(dt) , equals the rate at which salt enters the tank at the rate at which salt leaves the tank. Salt enters the tank at the rate of be lb/min. To determine the rate at which salt leaves the tank, we first calculate the volume of brine in the tank at any time t, which is the initial volume V_(0) plus the volume of brine added et minus the volume of brine removed ft. Thus, the volume of brine at any time is V_(0)+et-ft The concentration of salt in the tank at any time is Q//(V_(0)+et-ft) , from which it follows that salt leaves the tank at the rate of f(Q/(V_(0)+et-ft)) lb/min. Thus, (dQ)/(dt)=be-f(Q/(V_(0)+et-ft))Q=be A tank initially holds 100 L of a brine solution containing 20 lb of salt. At t=0, fresh water is poured into the tank at the rate of 5 L/min, while the well-stirred mixture leaves the tank at the same rate. Then the amount of salt in the tank after 20 min.

A person deposits Rs. X in savings bank account at the rate of 5% per annum and Rs. Y in fixed deposit at 10% per annum. At the end of one year, he gets Rs. 400 as total interest. If he deposits Rs. Y in savings bank account and Rs. X in fixed deposit, he would get Rs. 350 as total interest. Find the total amount he deposited.

In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e^(0.5) = 1.648) .

₹1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. the find interest amount after 20 years. For this complete the following activity.

NCERT TAMIL-SEQUENCES AND SERIES-Miscellaneous Exercise On Chapter 9
  1. If (a+bx)/(a-bx)=(b-cx)/(b-cx)=(c+dx)/(c-dx)( x ne 0) then show that ...

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  2. Let S be the sum, P the product and R the sum of reciprocals of n term...

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  3. The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respectiv...

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  4. If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in A.P., prove that a,...

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  5. If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n +...

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  6. If a and b are the roots of x^2 – 3x + p = 0 and c, d are roots of x^...

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  7. The ratio of the A.M. and G.M. of two positive numbers a and b, is m :...

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  8. If a, b, c are in A.P., b, c, d are in G.P. and 1/c,1/d,1/e are in A.P...

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  9. Find the sum of the following series up to n terms: (i) 5+55+555+......

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  10. Find the 20^(th) term of the series 2 xx 4 + 4 xx 6 + 6 xx 8 + ... + ...

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  11. Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 +......

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  12. If S1, S2, S3 are the sum of first n natural numbers, their squares a...

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  13. Find the sum of the following series up to n terms: 1^3/1+(1^3+2^3)/...

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  14. Show that (1 xx 2^(2) + 2 xx 3^(2) + ... +n xx (n + 1)^(2))/(1^(2) xx ...

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  15. A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and ag...

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  16. Shamshad Ali buys a scootor for Rs 22000. He pays Rs 4000 cash and agr...

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  17. A person writes a letter to four of his friends. He asks each one of t...

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  18. A man deposited Rs 10000 in a bank at the rate of 5% simple interest a...

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  19. A manufacturer reckons that the value of a machine, which costs him Rs...

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  20. 150 workers were engaged to finish a piece of work in a certain number...

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