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Let's calculate the cost price (CP) and selling price (SP) to determine the gain or loss and the percentage.

1. Cost Price (CP): The shopkeeper purchased 200 bulbs for Rs. 10 each. CP=Number of bulbs×Cost per bulbCP=Number of bulbs×Cost per bulb CP=200×10CP=200×10 CP=Rs.2000CP=Rs.2000

2. Selling Price (SP): 5 bulbs were fused and thrown away. So, the shopkeeper sold 200−5=195200−5=195 bulbs at Rs. 12 each. SP=Number of bulbs sold×Selling price per bulbSP=Number of bulbs sold×Selling price per bulb SP=195×12SP=195×12 SP=Rs.2340SP=Rs.2340

3. Gain or Loss: Gain or Loss=SP−CPGain or Loss=SP−CP Gain or Loss=2340−2000Gain or Loss=2340−2000 Gain=Rs.340Gain=Rs.340

4. Gain Percentage: Gain Percentage=(GainCP)×100Gain Percentage=(CPGain)×100 Gain Percentage=()×100Gain Percentage=()×100 Gain Percentage=17%Gain Percentage=17%

Therefore, the shopkeeper gained 17% by selling the bulbs.

To find the profit or loss percentage, follow these steps:

1. Cost Price (CP): The cost price is the sum of the purchase cost and the repair cost. CP=Purchase cost+Repair costCP=Purchase cost+Repair cost CP=Rs.2500+Rs.500CP=Rs.2500+Rs.500 CP=Rs.3000CP=Rs.3000

2. Selling Price (SP): The TV was sold for Rs. 3300. SP=Rs.3300SP=Rs.3300

3. Profit or Loss: Profit or Loss=SP−CPProfit or Loss=SP−CP Profit or Loss=3300−3000Profit or Loss=3300−3000 Profit=Rs.300Profit=Rs.300

4. Profit Percentage: Profit Percentage=(ProfitCP)×100Profit Percentage=(CPProfit)×100 Profit Percentage=()×100Profit Percentage=()×100 Profit Percentage=10%Profit Percentage=10%

Therefore, the profit percentage is 10%.

To calculate the amount to be paid on a loan compounded half-yearly, you can use the compound interest formula:

A=P(1+rn)ntA=P(1+nr)nt

where:

• AA is the amount (including principal and interest),
• PP is the principal amount (initial loan amount),
• rr is the annual interest rate (as a decimal),
• nn is the number of times interest is compounded per year,
• tt is the time the money is invested or borrowed for in years, and
• ntnt is the total number of compounding periods.

In this case:

• P=Rs.12000P=Rs.12000,
• r=10%r=10% or 0.100.10 (as a decimal),
• n=2n=2 (compounded half-yearly means twice a year),
• t=1.5t=1.5 years.

Plug these values into the formula:

A=12000(1+0.102)2×1.5A=12000(1+20.10)2×1.5

A=12000(1+0.05)3A=12000(1+0.05)3

Now, calculate the values:

A=12000×(1.05)3A=12000×(1.05)3

A≈12000×1.157625A≈12000×1.157625

A≈13951.50A≈13951.50

Therefore, the amount to be paid on the loan after 1½ years at 10% per annum compounded half-yearly is approximately Rs. 13,951.50.

It seems there might be a confusion in the given information. The population of a city is usually measured in terms of the number of people, not in rupees. If you meant to say the population of a city was 20,000 in 1997, and it increased at the rate of 5% per annum, then we can calculate the population at the end of the year 2000.

Let PP be the population in 1997.

Given that the population increases at a rate of 5% per annum, the growth factor is 1+5100=1.051+1005=1.05.

The population at the end of the year 2000 (t=2000−1997=3t=2000−1997=3 years) can be calculated using the formula for compound interest:

Population at the end of 2000=P×(1.05)3Population at the end of 2000=P×(1.05)3

Population at the end of 2000=20000×(1.05)3Population at the end of 2000=20000×(1.05)3

Now, calculate the value:

Population at the end of 2000≈20000×1.157625Population at the end of 2000≈20000×1.157625

Population at the end of 2000≈23152.50Population at the end of 2000≈23152.50

Therefore, the population of the city at the end of the year 2000 is approximately 23,152.50.

To find the discount and discount percentage, you can use the following formulas:

1. Discount (DD): D=Marked Price−Selling PriceD=Marked Price−Selling Price

2. Discount Percentage ((D%)): D%=(DiscountMarked Price)×100D%=(Marked PriceDiscount)×100

Given:

• Marked Price (MPMP) = Rs. 15600
• Selling Price (SPSP) = Rs. 12480

1. Discount (DD): D=15600−12480D=15600−12480 D=Rs.3120D=Rs.3120

2. Discount Percentage ((D%)): D%=()×100D%=)×100 D%=20%D%=20%

Therefore, the discount given is Rs. 3120, and the discount percentage is 20%.

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To calculate the current price of the box after a 20% increase from Rs 25,000 last year, you can use the following formula:

Current Price = Last Year's Price + (Last Year's Price * Increase Percentage)

In this case:

Current Price = Rs 25,000 + (Rs 25,000 * 0.20)

Current Price = Rs 25,000 + Rs 5,000

Current Price = Rs 30,000

Therefore, the current price of the box should be Rs 30,000.

To find the population of the city after 2 years with a 5% annual increase, you can use the formula for compound interest:

Future Population=Present Population×(1+Rate of Increase100)Number of YearsFuture Population=Present Population×(1+100Rate of Increase)Number of Years

In this case:

Future Population=20,00,000×(1+5100)2Future Population=20,00,000×(1+1005)2

Future Population=20,00,000×(1.05)2Future Population=20,00,000×(1.05)2

Future Population=20,00,000×1.1025Future Population=20,00,000×1.1025

Future Population≈22,05,000Future Population≈22,05,000

Therefore, the population of the city after 2 years would be approximately 22.05 lakh.

To find the amount that Ram will get after 18 months on a principal of ₹4,096 at a compound interest rate of 12.5% per annum, compounded half-yearly, we can use the compound interest formula:

A=P(1+rn)ntA=P(1+nr)nt

Where:

• AA is the amount after tt years,
• PP is the principal amount (initial amount),
• rr is the annual interest rate (in decimal form),
• nn is the number of times interest is compounded per year, and
• tt is the time in years.

In this case:

• P=₹4,096P=₹4,096,
• r=12.5100r=10012.5 (converted from percentage to decimal),
• n=2n=2 (compounded half-yearly, so twice a year),
• t=1812t=1218 (18 months converted to years).

A=4096(1+0.1252)2×1812A=4096(1+20.125)2×1218

A=4096(1+0.0625)3A=4096(1+0.0625)3

A=4096×1.1953125A=4096×1.1953125

A≈₹4,896.00A≈₹4,896.00

Therefore, Ram will get approximately ₹4,896.00 after 18 months.

To solve this problem, let's assume the population in the year 2001 was PP. We can then use the compound interest formula for population growth:

Population=P×(1+r100)tPopulation=P×(1+100r)t

Where:

• PP is the initial population,
• rr is the growth rate,
• tt is the time in years.

In this case: (i) To find the population in 2001, we need to find PP. We are given that the population increased to 54,000 in 2003 at a rate of 5% per annum. So, t=2t=2 years and r=5r=5.

54,000=P×(1+5100)254,000=P×(1+1005)2

Solving for PP: P=54,000(1.05)2P=(1.05)254,000

(ii) To find the population in 2005, we need to find the population after 4 years. t=4t=4 years and r=5r=5.

Population in 2005=P×(1+5100)4Population in 2005=P×(1+1005)4

Let's calculate:

(i) P=54,000(1.05)2(i) P=(1.05)254,000 (ii) Population in 2005=P×(1+5100)4(ii) Population in 2005=P×(1+1005)4

Please note that for accurate calculations, you should use a calculator or software.