Question

Help it's urgent ....
Number 3,4 and 5.

Answer 1

Hello........ ^_^

Q. (3).A man had total Rs. 75000.

(CASE 1)
He invested Rs. 35000 in a company which pay him 9% per annum.

(CASE 2)
and rest money = Rs 40000 (75000-35000) in another company which pay him 9.5%per annum.

(CASE 1)
Principal = Rs. 35000
Rate of interest = 9% per annum
Time (n) =2 years
$Amount \: = P {(1 + \frac{R}{100} )}^{n} \\ = 35000 {(1 + \frac{9 }{100} )}^{2} \\ = 35000 {( \frac{100 + 9}{100} )}^{2} \\ = 35000 {( \frac{109}{100} )}^{2} \\ = 35000 \times \frac{109}{100} \times \frac{109}{100} \\ = \frac{83167}{2} = 41583.50$
C.I = Amount - Principal
= 41583.50-35000
= Rs. 6583.50 ................(CASE 1)

(CASE 2)
Principal = Rs. 40000
Rate of interest = 9.5% per annum
Time (n) = 2 years
$Amount = P {(1 + \frac{R}{100} )}^{n} \\ = 40000 {(1 + \frac{9.5}{100} )}^{2} \\ = 40000 {( \frac{100 + 9.5}{100} )}^{2} \\ = 40000 {( \frac{109.5}{100} )}^{2} \\ = 40000 \times \frac{109.5}{100} \times \frac{109.5}{100} \\ = 4 \times 109.5 \times 109.5 \\ = 47961$
C.I = Amount - Principal
= 47961 - 40000
=Rs. 7691 ...................(CASE 2)

total C.I = C.I of (CASE 1 ) + C.I of (CASE 2)
= 6583.50+7961
= Rs. 14544.50




Q. (4)
Let Principal be 'P'
Rate of interest be 'R'
Time = (n1) = 2 years .................(CASE 1)
= (n2) = 3 years .................(CASE2)

(ACCORDING TO THE QUESTION)
in 2 years (CASE 1) Amount = Rs.7396
and in 3 years (CASE 2) Amount = Rs. 7950.70

$Amount (CASE \: 1)\ = P \: {(1 + \frac{R}{100} )}^{n1} \\ = P \: {(1 + \frac{R}{100} )}^{n1} \: = 7396......(CASE 1)$

$Amount of (CASE \: 2) = P { (1+ \frac{R}{100}) }^{n2} \\ = P { (1+ \frac{R}{100}) }^{n2} = 7950.70........... (CASE \: 2)$

$\frac{ (CASE \: 2\: )}{ (CASE \: 1)} = \frac{P {(1 + \frac{R}{100} )}^{3} }{P {(1 + \frac{R}{100} )}^{2} } = \frac{7950.70}{7396} \\ = (1 + \frac{R}{100} ) = \frac{79507}{73960} \\ = \frac{R}{100} = \frac{79507}{73960} - 1 \\ \\ = \frac{R}{100} = \frac{79507 - 73960}{73960} \\ \\ = \frac{R}{100} = \frac{5547}{73960} \\ \\ = R \: = \frac{5547}{73960} \times 100 \\ \\ = R \: = \frac{544700}{73960} \\ \\ = R = 7.5 \: \: \: \: \: (7 \frac{1}{2} )$
Rate of interest = 7.5% per annum.





Q. (5)
Principal = Rs.200000
Rate of interest
= (first year ) = (a) = 5% per annum
= (second year) = (b) = 8% per annum
= (third year) =(c) = 12% per annum

$Amount = P(1 + \frac{a}{100} )(1 + \frac{b}{100} )(1 + \frac{c}{100} ) \\ = 200000(1 + \frac{5}{100} )(1 + \frac{8}{100} )(1 + \frac{12}{100} ) \\ = 200000(1 + \frac{1}{20} )(1 + \frac{2}{25} )(1 + \frac{3}{25} ) \\ = 200000( \frac{20 + 1}{20} )( \frac{25 + 2}{25} )( \frac{25 + 3}{25} ) \\ = 200000 \times \frac{21}{20} \times \frac{27}{25} \times \frac{28}{25} \\ = 200000 \times \frac{15876}{12500} \\ = 254016$
Amount = Rs. 254016

C.I = Amount - Principal
= 254016 - 200000
= Rs. 54016 ( total profit)

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