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4 years ago

Please explain me question no 18 with standard of class 9

Mathematics

1 answer:

Lelechka [254]4 years ago

5 0

Answer:

10%

Step-by-step explanation:

If Rs. 40000 amounts to Rs. 48620.25 in 2 years, and the interest compounded half-yearly, then we have to find the rate of interest per annum.

Let the principal is getting an x% interest rate per annum.

Therefore, half-yearly interest rate is $\frac{x}{2}$ %.

Again, the interest will be compounded for (2 × 2) = 4 times within the period of 2 years.

Therefore, from the formula of compound interest, we have

$S = P(1 + \frac{r}{100} )^{n}$

where S = Sum, P = Principal, r = rate of interest for the interval of compounding, and n = number of times of compounding.

So, $48620.25 = 40000(1 + \frac{x}{2 \times 100} )^{4}$

⇒ $(1 + \frac{x}{2 \times 100} ) = 1.05$

⇒ $\frac{x}{2 \times 100} = 0.05 = \frac{1}{20}$

⇒ x = 10%.

Therefore, the rate of interest per annum is 10%. (Answer)

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so x becomes 3x

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Take log on both sides

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Use log property and move exponent before log

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Divide both sides by x

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1.584740= 1+r

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so equation becomes

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Answer is option C

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Proof -

As given,

In ΔOPQ, PQ = 17, QO = 9, and OP = 15.

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