(i) Round off the bill to the nearest tens of Rs. 577.80, i.e., to Rs. 580.
(ii) Find 20% of this,
Rs.\(\frac { 20 }{ 100 } \)x 580 = Rs.116.
(iii) Therefore estimated 20% of the same bill amount is Rs. 116 or Rs. 120 (rounded off to the nearest tens).

Principal = RS. 21,000
Reduction = 5% of RS. 21000 per year
\(= \ RS. \frac{21000 \times 5 \times 1}{100}=\ RS. 1050\)
value at the end of 1 year = RS. 21000 – RS. 1050 = RS. 19,950

There is 5% increase in population every year, so every new year has new population. Thus, we can say it is increasing in compounded form.
Population in the beginning of 1998 = 20000 (we treat this as the principal for the 1st year)
Increase at 5% = \(=\frac{5}{100} \times 20000=1000\)
Population in 1999 = 20000 + 1000 = 21000
Increase at 5% \(=\frac{5}{100} \times 21000=1050\)
Population in 2000 = 21000 + 1050
= 22050
Increase at 5% = \(\frac{5}{100} \times 22050\)
= 1102.5
At the end of 2000 the population = 22050 + 1102.5 = 23152.5
or, Population at the end of 2000 = 20000 \(\left(1+\frac{5}{100}\right)^{3}\)
\(=20000 \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20}\)
= 23152.5
So, the estimated population = 23153.

Rs 23328;Rs 3328

Overall CP of each fan = RS. 1200. One is sold at a loss of 5%.
This means if CP is RS. 100, SP is RS. 95.
Therefore, when CP is RS. 1200, then SP = RS. \(\frac{95}{100} \times 1200=\text { Rs. } 1140\)
Also second fan is sold at a profit of 10%.
It means, if CP is RS. 100, SP is RS. 110.
Therefore, when CP is RS. 1200, then SP = RS. \(\frac{110}{100} \times 1200=\ Rs. 1320\)

Cost price of 200 bulbs = RS. 200 x 10 = RS. 2000
5 bulbs were fused. Hence, number of bulbs left = 200 – 5 = 195
These were sold at RS. 12 each.
The SP of 195 bulbs = RS. 195 x 12 = RS. 2340
He obviously made a profit (as SP > CP).
Profit = RS. 2340 – RS. 2000 = RS. 340
On RS. 2000, the profit is RS. 340. 
Profit \(=\frac{340}{2000} \times 100 \%=17 \%\)

\(\because\) Present population (P) = 20 lakh = 20,00,000
Rate of increased (R) = 5% p.a.
Time = 2 years \(\Rightarrow\) n = 2
\(\therefore\)Population after 2 years = P\([1+{R\over100}]^n\)
= 20,00,000 \([1+{5\over100}]^2=2000000[{21\over20}]^2\)
= 2000000 x \({21\over20}\times {21\over20}\)
= 5000 x 21 x 21 = 22,05,000
Thus, the population of the city after 2 years
= 22,05,000

Let the cost of TV before VAT (or the original cost) be Rs 100
\(\therefore\) VAT = 12% of the original cost
= \(12\over100\) x Rs 100 = Rs 12
\(\therefore\)Cost of TV including VAT = Rs 100 +Rs12 = Rs 112
If price including VAT is Rs 112, then original cost = Rs 100
If price including VAT is Rs 89,600, then original
cost = \(100\over112\) x 89,600 = Rs 80,000

Total cost price = Rs 5000 + Overhead expenses
= Rs 5000 + Rs 400 = Rs 5400
Selling price = Rs 6300
\(\because\)Selling price > Cost price
\(\therefore\) Profit = Rs 6300 - Rs 5400 = Rs 900
or Profit per cent = \(900\over 5400\) x 100%
= \(50\over 3\)% = 16\({2\over3}\)%
Thus, she earned a profit of 16\({2\over3}\) %

The price includes the VAT (The Value Added Tax). A 10% VAT means, if the price without VAT is Rs 100, then
price including VAT is RS. 110.
Now, when price including VAT is Rs 110, original price is Rs 100.
Hence, when price including tax is 3300, the original price = Rs \(\frac{100}{110}\times 3300\)=Rs 3000

Combined cost price = 15000 + 15000 = Rs 30000
Profit on one washing machine = 15% of 15000 = \(\frac{15}{100}\times 15000 = \)Rs 2250
SP of one washing machine = CP + Profit = Rs(15000+2250)=Rs 17250
Loss on other washing machine = 15% of15000 \(\frac{15}{100}\times 15000 = \) Rs 2250
∴ SP of the other washing machine = CP - Loss = 15000 - 2250 = Rs 12750
Combined SP = Rs (17250 + 12750) = Rs 30000
∵ Combined CP = Combined SP
Hence, no overall profit or loss.

CP of iron = Rs 560, expense = Rs 80, CP of iron = Rs (560 +80) = Rs 640 and profit = 5% of 640 = Rs 32
∴  SP = CP + Profit = Rs (640 +32) = Rs 672

(a) CP of hair dryer = Rs (500 + 50) = Rs 550, Profit = 5%of 550 = Rs 27.5
∴  SP = CP + Profit = Rs (550 + 27.5) = Rs 577.5

(i) Round off the bill to nearest tens of Rs 577.80 i. e. Rs 580.
(ii) To find 15% of this, we get 10% of the bill i.e. \(\frac{10}{100}\times 580\)= Rs 58
(iii) Take half of this i.e .\(\frac{1}{2}\times 58=29\)
(iv) Add the amounts of (ii) and (iii), we get 58 + 29 = Rs 87
Thus, our bill amount is reduced by Rs 87 and we have to pay Rs 493 or Rs 495 approximately.

We know that,
Discount = Marked price - Sale price
Sale price = Marked price - Discount
∵ Marked price = Rs 650                   [given]
Discount = 10% of Rs 650 =\(\frac{10}{100}\times 650\)=65
∴ Sale price = Marked price - Discount = Rs (650 - 65) = Rs 585