Rs 330

Given, principal (P) =Rs 1024000
∴ Rate of interest (R) = 5% and time (n) = 1yr
For half-yearly,
n = 1 x 2 = 2 and R = \(\frac{5}{2}\%=2.5%\)
∴ Amount=P\((1+\frac{R}{100})^{n}=1024000\times (1+\frac{2.5}{100})^{2}\)
=1024000\(\times \frac{1025}{1000}\times \frac{1025}{1000}\)=  Rs 1024000
ஃ Compound interest = Amount - Principal
= Rs 1075840 - Rs 1024000
= Rs 51840
So, amount he have to pay is Rs 1075840 and compound interest paid is Rs 51840.

From the given information, we have

Passing percentage of students of the Class X examination in year 2007-08
=\(\frac{Number of students passed}{Number of students appeared}\times 100 \)
\(=\frac{88151}{105332}\times 100\)= 89.45%
Passing percentage of students of the Class X examination in year 2008-09 = \(\frac{103804}{116054}\times 100\) = 89.45%
It is clear that in year 2008-09, passing percentage is increased by (89.45% - 83.69%) i.e. 5.76%.

Rs 2325

Case I principal (P) = Rs10000, rate (R) = 10% ,
time (n) = 1\(\frac{1}{2}\)yr = \(\frac{3}{2}\)yr
Forhalf-yearly
n = \(\frac{3}{2}\)ｘ2 = 3 yr and R=\(\frac{10}{2}\)% = 5%
∴ Amount (A) P = \((1+\frac{R}{100})^{n}=10000(1+\frac{5}{100})^{3}\)
=\(10000(\frac{100+5}{100})^{3}=10000(\frac{105}{100})^{3}\)
\(=10000 (\frac{21}{20})^{3}=10000\times\frac{21}{20}\times\frac{21}{20}\times\frac{21}{20}\)
=\(\frac{10\times21\times21\times21}{2\times2\times2}=\frac{5\times21\times21\times21}{4}\)
=\(\frac{46305}{4}\) = Rs 11576.25
∴ Compound interest = Amount (A) - Principal (P)
= Rs (11576.25 -10000) = Rs 1576.25
CaseII When interest is compounded annually, then amount for 1 yr,
\(A=P(1+\frac{R}{100})^{n}=10000(1+\frac{10}{100})^{1}\)
=\(10000(\frac{100+10}{100})=10000\times \frac{110}{100}=\) Rs 11000
Since,amount at the end of 1 yr is Rs 11000. So, the principalfor the next \(\frac{1}{2}\)yr is Rs 11000.
∴ SI = \(\frac{P\times R \times T}{100}=\frac{11000\times 10\times 1}{100\times 2}=110\times 5\) = Rs 550
So, amount at the end of 1\(\frac{1}{2}\)year = Rs 11000 + Rs 550
= Rs 11550
∴ Compound interest = Amount (A) - Principal (P)
= Rs (11550 -10000) = Rs 1550
Hence, the interest in the first case is greater than in the
second case i.e. Rs (1576.25 -1550) = Rs 26.25.

Here, P = Rs 8000, T = 1 year, R = 9% p.a.
Interest is compounded half yearly,
\(\therefore\)T = 1 year = 2 half years
R = 9% p.a =\(9\over2\)% half yearly
\(\therefore\)Amount = p\((1+{R\over100})^n\)
= Rs 8000 x\((1+{9\over200})^2\)
= 8000 x \({209\over200}\times{209\over200}\) =Rs \({2 \times 209 \times 209\over 10}\)
= Rs \(87362\over10\)= Rs 8736.20
CI = Rs  8736.20 - Rs 8000 =Rs 736.20

Here, principal (P) = Rs10800, time (n) = 3 yr
and rate (R) = 12 \(\frac{1}{2}\)% = \(\frac{25}{2}\)%
ஃ Amount (A) = P\((1+\frac{R}{100})^{n}=10800(1+\frac{\frac{25}{2}}{100})^{3}\)
= 10800\((1+\frac{25}{2\times 100})^{3}\)
= \((1+\frac{25}{ 100})^{3}\)
= 10800\((\frac{200+25}{200})^{3}=10800(\frac{225}{200})^{3}\)
= 10800\(\times \frac{9}{8}\times \frac{9}{8}\times \frac{9}{8}\)=675\(\times 9 \times \frac{9}{4}\times \frac{9}{8}\)
= \( \frac{492075}{32}\) = Rs 15377.34
∴ Compound interest = Amount (A) - Principal(P)
= 15377.34- 10800
= Rs 4577.34

Rs 2800

Letcost price of Ist buffalo = Rs x
Given,gain per cent on Ist buffalo = 5%
∴ Gain amount on Ist buffalow = 5% of cost price of I st buffalo
= 5% of Rs x=Rs\((\frac{5}{100}\times x)\)=Rs \(\frac{5x}{100}\)
Selling price of Ist buffalo = Cost price of Ist buffalo + Gain amount on Ist buffalo
= Rs \((x+\frac{5x}{100})\)
= Rs \((\frac{100x+5x}{100})=Rs \frac{105x}{100}\)
Butselling price ofIst buffalo = Rs 20000
∴ \(\frac{105x}{100}\) = 2000 ⇒ 105x = 20000ｘ100
⇒ x = \(\frac{20000\times100}{105}⇒ x=\frac{400000}{21}\)
⇒ x = Rs 19047.62
Letcostprice ofIInd buffalo be Rs y.
Given,lossper cent on IInd buffalow = -10%.
Lossamount on IInd buffalo = 10% of cost price of IInd buffalo
= 10% of Rs y =Rs \((\frac{10}{100}\times y)\)=\(\frac{Rs 10 y}{100}\)
Sellingprice of IInd buffalo = Cost price of IInd buffalo - Loss amount on the buffalo
=Rs \((y-\frac{10 y}{100})=Rs (y-\frac{10 y}{100})\)
=Rs \(\frac{100y-10y}{100}=Rs \frac{90 y}{100}\)
But selling price ofIInd buffalo = Rs 20000
∴ \(\frac{90 y}{100}\)=20000 ⇒ 90y =20000ｘ100
⇒ \(y=\frac{20000\times100}{90}\)
⇒ y=\(\frac{200000}{9}\)
⇒ y=Rs 22222.22
∴  Total cost price of both buffaloes = Rs (x + y)
= Rs 19047.62 + Rs 22222.22 = Rs 41269.84
∴ Total selling price of both buffaloes = Rs 20000 + Rs 20000
= Rs 40000
∴ SP< CP
∴ Loss amount on both buffaloes
Cost price of both buffaloes - Selling price of both buffaloes
= Rs 41269.84 - Rs 40000
= Rs 1269.84
Hence, overall loss is Rs 1269.84.

41.66=42

400

Let Chameli had total money be Rs x.
Percentage of money spent by Chameli = 75%
Chameli had left money after spending = (100 - 75)%
= 25%
But money left = Rs 600             [given]
∴ 25% of x = 600
⇒ \(\frac{25}{100}\times x=600 \Rightarrow x=\frac{600\times100}{25}=2400\)
Hence, Chameli had Rs 2400 in the beginning.
 Alternate Method
Let total money with Chameli at the beginning be Rs 100.
Expenditure money = 75% of total money
\(= Rs(\frac{75}{100}\times100)=Rs 75\)
Money left = Rs 100 - Rs 75=Rs 25
Now, if saving is Rs 25, then money at the beginning = Rs 100 
If saving is Rs 1, then money at the beginning = Rs \(\frac{100}{25}\)
If saving is Rs 600, then money at the beginning
\(= Rs (\frac{100}{25}\times 600)=Rs(4\times 600)= Rs 2400\)
Hence, total money at the beginning with Chameli was Rs 2400.