2.1 Math 1-5 Class 8

2.1 Math 1-5 Class 8

Math Class 8

Exercise 2.1 (1-5)

1. On selling a commodity, the proﬁt of a wholesale seller is 20% and the profit of retail seller is 20%. If the retail selling price of the commodity is Tk. 576, what is the cost price of the wholesaler?

একটি পণ্যদ্রব্য বিক্রয় করে পাইকারি বিক্রেতার ২০% এবং খুচরা বিক্রেতার ২০% লাভ হয়। যদি দ্রব্যটির খুচরা বিক্রয়মূল্য ৫৭৬ টাকা হয়, তবে পাইকারি বিক্রেতার ক্রয়মূল্য কত?

Solution:

Given,

$egin{array}{l}{ ext { The selling price of commodity is } 576 ext { taka }} \ { ext { Profit of a wholesale seller is } 20 \%} \ { ext { Profit of a retail seller is } 20 \%}end{array}$

$egin{array}{l}{ ext { Cost price of wholesale seller }=?} \ { ext { In } 20 \% ext { profit selling price of retail seller }} {=(100+20) ext { taka }} {=120 ext { taka }}end{array}$

$egin{array}{l}{ ext { If selling price } 120 ext { taka then cost price is } 100 ext { taka }} \ { herefore ext { If selling price } 1 ext { taka then cost price is } frac{100}{120} ext { taka }}end{array}$

$herefore ext { If selling price } 576 ext { taka then cost price }$ $frac{100 imes 576}{120}=480$

$egin{array}{l}{ ext { Therefore, selling price of wholesale seller } 480} { ext { taka }} \ { ext { In } 20 \% ext { profit selling price of wholesale seller }} \ {=(100+20)=120 ext { taka }}end{array}$

$herefore ext { If selling price } 480 ext { taka then cost price }$ $frac{100 imes 480}{120}=400 Tk$

$herefore ext { cost price of wholesale seller } 400 Tk$

Answer: 400 Taka

2. A shopkeeper sold some amount of pulses for Tk 2,375 at the loss of Tk. 5%.What would be the selling price of pulses to make a proﬁt of Tk. 6% ?

একজন দোকানদার কিছু ডাল ২৩৭৫.০০ টাকায় বিক্রয় করায় তার ৫% ক্ষতি হলো। ঐ ডাল কত টাকায় বিক্রয় করলে তার ৬% লাভ হতো ?

Solution:

$egin{aligned} ext { In } 5 \% ext { loss, selling price } &=(100-5) ext { taka } \ &=95 ext { taka } end{aligned}$

$egin{aligned} ext { In } 6 \% ext { profit, selling price } &=(100+6) ext { taka } \ &=106 ext { taka } end{aligned}$

$egin{array}{l}{ ext { If } 95 ext { taka is selling price then cost price is } 100 ext { taka }} \ { herefore ext { If } 1 ext { taka is selling price then cost price is } frac{100}{95} ext { taka }}end{array}$

$ext { If, }2375 ext { taka is selling price then cost price is }$ $frac{100 imes 2375}{95}$ $=2500 Tk$

$egin{array}{l}{ ext { Again, }} \ { ext { When } 100 ext { taka is cost price then selling price is 106 Taka}}end{array}$

$herefore ext { When 1 Taka is cost price then selling price is}$ $frac{106}{100} Taka$

$herefore ext { When 2500 taka is cost price then selling price is}$ $frac{106 imes 2500}{100} Taka$

$=2650 Taka$

$herefore ext { The selling price would be } 2650 Taka$

Answer: 2650 Taka

3. An equal number of bananas is bought at 10 and 15 pieces per Tk.30 and all the bananas are sold at 12 pieces per Tk. 30. What will be the percentage of proﬁt

or loss?

৩০ টাকায় ১০টি দরে ও ১৫টি দরে সমান সংখ্যক কলা ক্রয় করে সবগুলো কলা ৩০ টাকায় ১২টি দরে বিক্রয় করলে শতকরা কত লাভ বা ক্ষতি হবে?

Solution:

$egin{array}{l}{ ext { The L.C.M of } 10,15,12 ext { is } 60} \ { ext { Let, }} \ { ext { The cost price of } 10 ext { banana is } 30 ext { taka }} \ { herefore ext { The cost price of } 1 ext { banana is } frac{30}{10} ext { taka }}end{array}$

$herefore ext { The cost price of } 60 ext { bananas is } frac{30 imes 60}{10} Taka = 180 Taka$

$egin{array}{l}{ ext { Again, }} \ { ext { The cost price of } 15 ext { bananas is } 30 ext { taka }} \ { herefore ext { The cost price of } 1 ext { bananas is } frac{30}{15} ext { taka }}end{array}$

$egin{array}{r}{ herefore ext { The cost price of } 60 ext { bananas is } frac{30 imes 60}{15} mathrm{Tk} ext { . }} \ {=120 mathrm{Taka}}end{array}$

$egin{aligned} herefore ext { The cost price of }(60+60) & ext { or, } 120 ext { bananas } \ &=(180+120)=300 ext { taka } end{aligned}$

$egin{array}{l}{ ext { But, }} \ { ext { The selling price of } 12 ext { bananas is } 30 ext { taka }} \ { herefore ext { The selling price of } 1 ext { banana is } frac{30}{12} ext { taka }}end{array}$

$egin{aligned} herefore ext { The selling price of } 120 ext { bananas is } & frac{30 imes 120}{12} ext { Tk. } \ &=300 ext { taka } end{aligned}$

$egin{array}{l}{ herefore ext { So the cost price and selling price of } 120} { ext { bananas is } 300 ext { taka }}end{array}$

Answer: There is no profit or loss.

4. What will be the proﬁt for Tk. 2,000 in 5 years if the percentage of proﬁt is Tk. 10.50 per annum?

বার্ষিক শতকরা মুনাফার হার ১০.৫০ টাকা হলে, ২০০০ টাকার ৫ বছরের মুনাফা কত হবে?

Solution:

$egin{array}{l}{ ext { In } 100 ext { Taka } 1 ext { year profit is } 10.50 ext { taka }} \ { herefore ext { In } 1 ext { Taka } 1 ext { year profit is } frac{10.50}{100} ext { taka }}end{array}$

$egin{aligned} herefore ext { In } 2000 ext { taka } 5 ext { years profit is } & frac{10.50 imes 2000 imes 5}{100} ext { Tk. } \ &=frac{1050 imes 2000 imes 5}{100 imes 100} mathrm{Tk} \ &=1050 mathrm{taka} end{aligned}$

$herefore ext { Profit is } 1050 Taka$

Answer: Profit is 1050 Taka

Alternative:

$egin{array}{c}{ ext { Given, Principal }=mathrm{P}=2000 mathrm{taka}} \ { ext { Time }=mathrm{n}=5 ext { years }} \ { ext { Profit }=mathrm{r}=10.50 \%}end{array}$

$egin{aligned} ext { We know, Total profit, } & ext { I = Pnr } \ I &=2000 imes 5 imes 10.50 \% \ &=2000 imes 5 imes 10.50 imes frac{1}{100} \ &=1050 ext { taka } end{aligned}$

Answer: Profit is 1050 Taka

5. How much less will be the proﬁt of Tk. 3,000 in 3 years if the percentage of proﬁt per annum is decreased from Tk. 10 to Tk. 8?

বার্ষিক মুনাফা শতকরা ১০ টাকা থেকে কমে ৮ টাকা হলে, ৩০০০ টাকার ৩ বছরের মুনাফা কত কম হবে?

Solution:

$egin{array}{l}{ ext { For } 100 ext { taka in } 1 ext { year profit decreased by (10-8) taka = 2 taka }} \ { herefore ext { For } 1 ext { taka in } 1 ext { year profit decreased by } frac{2}{100} ext { Tk }}end{array}$

$egin{array}{l}{ herefore ext { For } 3000 ext { taka in } 3 ext { years profit decreased by }} {frac{2 imes 3000 imes 3}{100} ext { taka=180taka }} \ { herefore ext { Profit decreased } 180 ext { taka }}end{array}$

Answer: 180 Taka

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