**Ex: Rodrick Gomage borrowed Tk. 10000 for 3 years and Tk. 15000 for 4 years from a bank and paid Tk. 9900 in total as profit. In both cases if the rate of profit is same , find the rate of profit.**

Solution:

Let,

The percentage of profit x Taka

In 100 Taka 1 year profit is x Taka

∴In 1 Taka 1year profit is x/100 Taka

∴In 10000 Taka 3 years profit is (x×10000×3)/100 Taka

=300x Taka

Again,

In 100 Taka1 year profit is x taka

∴In 1 Taka 1 year profit is x/100 Taka

∴In 15000 Taka 4 years profit is (x×15000×4)/100 Taka

=600x Taka

According to the question,

300x+ 600x = 9900

Or, 900x= 9900

Or, x = 9900/900

∴x= 11 Taka

∴Profit percentage 115

Ans: 11% .

**Ex: Some principal becomes its double as profit- principal in 6 years as the same percentage of profit. In how many years will it be trice of it as profit- principal at the same percentage of profit?**

Solution:

Let, Principal is 100 Taka

∴In 6 years profit principal (100×2)=200 Taka

∴6 years profit =(200-100)=100 Taka

In a certain time profit principal is =(100×3)=300 Taka

In a certain time profit is = (300-100) Taka=200 Taka

100 Taka profit in 6 years

∴ 1 Taka profit in 6/100 years

∴ 200 Taka profit in (6×200)/100 years

=12 years

Ans: 12 years.

**Ex: The profit- principal for a certain period of time is Tk. 5600 and the profit is 2/5 of the principal. If the percentage of profit is Tk. 8 , find the time.**

Solution:

Let, Principal = 100 Taka

∴ profit = (2/5 of 5600) Taka

= 5600×2/5 Taka

=2240 Taka

In 100 Taka 1 year profit is 8 Taka

∴ In 1 Taka 1 year profit is 8/100 Taka

∴ In 5600 Taka 1 year profit is (8×5600)/100 = 448 Taka

448 Taka profit is 1 year

∴1 Taka profit is 1/448 year

∴ 2240 Taka profit is (1× 2240)/448 year

=5 years

Ans: 5 years.

**Ex: After having the pension, Mr. Jamil bought pension savings certificate of Tk. 10 lac for three years term on the basis of having the profit in three months` interval. If the percentage of profit is 12% per annum, what amount of profit will he get at first installment, that is, after three months?**

Solution:

Here

Principal = 10,00,000 Taka

Rate of profit = 12%

We know, 1 year =12 months

For 100 Taka in 12 month profit is 12 Taka

∴ For 100 Taka in 1 month profit is 12/12 Taka

∴For 1 Taka in 1 month profit is 12/(12×100) Taka

∴ For 10,00,000 Taka in 3 months profit is (12×10,00,000×3)/(12×100) Taka

=30,000 Taka

Therefore the required amount of profit is 30,000 Taka.

Ans: 30,000 Taka.

**Ex: A person makes a profit of 10% and 25% of the quantity and a loss of 20% on the rest. What is the percentage gain or loss on the** whole?

Solution:

Let total quantity = Tk. 100

25% of 100 = 25

Let, Cost per quantity = Tk. 100

∴ cost price of 25= 25×100 = Tk. 2500

At 10% profit

Sell price of 25 quantity = 2500+ 10% ×2500= 2500+(10/100)× 2500

= 2500+250=2750

Remaining quantity 100-25= 75

Cost price of 75 quantity= Tk. 7500

Sell price= 7500-(20/100)×7500=7500-1500= Tk. 6000

Total cost = Tk. (2500+7500)= Tk. 10,000

Total sell = Tk.(2750+6000) = Tk. 8750

∴ Loss= (10,000-8750)

=Tk. 1250

∴ The percentage of loss= (1250×100)/10,000= 12.5 %

Ans: 12.5%

**Ex: A 5% monthly salary increase resulted in a salary increase of tk. 6000 per year for an employee. What was his monthly salary before the increase?**

Solution:

Increase per year 6000 Tk.

So increase per month= 6000/12 = 5000 Taka

Therefore, per month salary of 5% is 500 Tk

Monthly salary ×5%= 500

∴ monthly salary = (500×100)/5 = 10,000

Ans:10,000 Taka.

**Ex: Rice is now being sold at Taka 20 per kg. During last month its rate was Taka 16 per kg. By how much percent should a family reduce its consumption so as to keep the expenditure fixed?**

Solution:

Let, P and Q be the prices if rice at previous and present respectively.

∴ The cost of previous month = 16 P and present month= 20Q

At cost is unchanged, 16P= 20Q

∴Q= 0.8 P

∴ at present they consume 0.8 times of previous month; i.e. 80%

∴ Reduction in consumption = (100-80)% = 20%

Ans: 20%

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