2.1 Math 16-20 Class 8

2.1 Math 16-20 Class 8

Math Class 8

Exercise 2.1 (16-20)

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

একই হার মুনাফায় কোনও আসল ৬ বছরে মুনাফা-আসলে দ্বিগুণ হলে, কত বছরে তা মুনাফা-আসলে তিনগুণ হবে?

Solution:

Let, Principal = P

$egin{array}{l}{ herefore ext { For } 1^{ ext { st }} ext { case, profit - principal, } A=2 P} \ { herefore ext { profit, } I=A-P=2 P-P=P}end{array}$

$egin{array}{c}{ ext { Now, for } 6 ext { years, }} \ {mathrm{I}=operatorname{Pnr}} \ { ext { or, } mathrm{r}=frac{mathrm{I}}{mathrm{Pn}}=frac{mathrm{P}}{mathrm{P} imes 6}=frac{1}{6}}end{array}$

$egin{array}{l}{ ext { Again, For } 2^{ ext { nd }} ext { case, profit - principal, } A=3 P} \ { herefore ext { Profit, } I=3 P-P=2 P ext { . }} \ { ext { Now, I }= ext { Pnr }}end{array}$

$egin{array}{l}{ ext { or, } 2 mathrm{P}=mathrm{P} imes mathrm{n} imes frac{1}{6}} \ { herefore mathrm{n}=12} \ { herefore 12 ext { years will be required. }}end{array}$

Answer: 12 Years

17. The proﬁt—principal for a certain period of time is Tk. 5,600 and the proﬁt is 2/5 of the principal. If the percentage of proﬁt is Tk. 8, ﬁnd the time.

কোনো নির্দিষ্ট সময়ের মুনাফা-আসল ৫৬০০ টাকা এবং মুনাফা, আসলের ২/৫ অংশ। মুনাফা বার্ষিক শতকরা ৮ টাকা হলে, সময় নির্ণয় কর৷

Solution:

$egin{array}{l}{ ext { Given, }} \ { ext { Principal, } mathrm{P}=5600 mathrm{Tk}} \ \ { ext { Profit, } mathrm{I}=left(frac{2}{5} ext { of } 5600 ight) mathrm{Tk}} \ \ {=frac{2 imes 5600}{5}} \ \ {=2240 mathrm{Tk}}end{array}$

$egin{array}{l}{ ext { Rate of profit, } r=8 \%=frac{8}{100}} \ { ext { Time period, } n=?} \ \ { ext { We know, } I=P ext { nr }} \ \ {=frac{2240 imes 100}{5600 imes 8}=5} \ \ { herefore ext { Time period is } 5 ext { years. }}end{array}$

Answer: 5 Years

18. After having the pension, Mr. Jamil bought pension savings certiﬁcates of Tk. 10 Iac for ﬁve 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 the ﬁrst installment, that is, after ﬁrst three months?

জামিল সাহেব পেনশনের টাকা পেয়ে ১০ লাখ টাকার তিন মাস অন্তর মুনাফা ভিত্তিক ৫ বছর মেয়াদি পেনশনের সঞ্চয়পত্র কিনলেন৷ বার্ষিক যুনাফা ১২% হলে, তিনি ১ম কিস্তিতে, অর্থাৎ প্রথম ৩ মাস পর কত মুনাফা পাবেন?

Solution: Here,

$egin{aligned} ext { Principal, } P=& 10,00,000 ext { Tk. } \ \ ext { Rate of profit, } r=12 \%=frac{12}{100} \ \ ext { Time period, } n=3 ext { months } &=frac{3}{12} \ \ &=frac{1}{4} ext { years. } end{aligned}$

$egin{aligned} herefore ext { Profit, I= } &= ext { Pnr } \ &=10,00,000 imes frac{1}{4} imes frac{12}{100} \ &=30,000 end{aligned}$

The amount of profit is 30,000 Tk

Answer: 30,000 Tk

19. A fruit seller bought some bananas at the cost of Tk. 36 for 12 pieces from Jessore and Tk. 36 for 18 pieces from Kustia, He bought equal pieces of bananas both from Jessore and Kustia. His salesman sold the bananas at Tk. 36 for 15 pieces.

A. What was the cost price of 100 pieces from Jessore?

B. If the salesman sold all bananas, how much would be proﬁt or loss?

C. If the fruit seller wants to make 25% proﬁt. What would be the selling price for 4 pcs of banana?

একজন ফল ব্যবসায়ী যশোর থেকে ৩৬ টাকায় ১২টি দরে কিছু সংখ্যক এবং কুষ্টিয়া থেকে ৩৬ টাকায় ১৮টি দরে সমান সংখ্যক কলা খরিদ করল। ব্যবসায়ীর বিক্রয়কর্মী ৩৬ টাকায় ১৫টি দরে তা বিক্রয় করলেন৷

ক। ব্যাবসায়ী যশোর থেকে প্রতিশ কলা কি দরে ক্রয় করেছিলেন?

খ। বিক্রয়কর্মী সবগুলো কলা বিক্রয় করলে শতকরা কত লাভ বা ক্ষতি হবে?

গ। ব্যবসায়ী ২৫% লাভ করতে চাইলে প্রতি হালি কলা কি দরে বিক্রয় করতে হবে?

Solution:

(a)

$egin{aligned} ext { The cost price of } 12 ext { bananas is } 36 ext { taka. } \ herefore ext { the cost price of } 1 ext { banana is } frac{36}{12} ext { taka. } \ &=3 ext { taka } end{aligned}$

$egin{aligned} herefore ext { the price of } 100 & ext { pieces of banana } \ &=(3 imes 100) mathrm{Tk} .=300 mathrm{Tk} end{aligned}$

Ans: 300 TK

(b)

$egin{array}{l}{ ext { The L.C.M of } 12,18 ext { and } 15 ext { is } 180 ext { . }} \ { ext { From answer (a), for bananas bought from }} { ext { Jessore, }} \ \ { ext { The cost price of } 1 ext { banana is } 3 ext { taka }}end{array}$

$egin{aligned} herefore ext { The cost price of } 180 ext { bananas is }(180 imes 3) mathrm{Tk} \=& 540 ext { taka } end{aligned}$

$egin{array}{l}{ ext { Again, for bananas bought form Kushtia, }} \ { ext { The cost price of } 18 ext { bananas is } 36 ext { taka }} \ \ { herefore ext { The cost price of } 1 ext { banana is } frac{36}{18} ext { taka }}end{array}$

$egin{aligned} herefore ext { The cost price of } 180 ext { bananas is } \ & frac{36 imes 180}{18} ext { taka } \=& 360 ext { taka } end{aligned}$

$egin{aligned} ext { Therefore, } \ ext { The cost price of }(180+180) &=360 ext { bananas } \ &=(540+360) \ &=900 ext { taka. } end{aligned}$

$egin{array}{l}{ ext { But, }} \ { ext { The selling price of } 15 ext { bananas is } 36 ext { taka }} \ \ { herefore ext { The selling price of } 1 ext { banana is } frac{36}{15} ext { taka }}end{array}$

$egin{aligned} herefore ext { The selling price of } 360 & ext { bananas is } \ & frac{36 imes 360}{15} ext { taka } \ &=864 ext { taka } end{aligned}$

$egin{aligned} ext { So, there will be loss in selling bananas. } \ ext { Loss } &= ext { cost price - selling price } \ &=900-864 ext { taka } \ &=36 ext { taka. } end{aligned}$

$egin{array}{l}{ ext { For cost price } 900 ext { taka loss }=36 ext { taka }} \ { herefore ext { For cost price } 1 ext { taka loss }=frac{36}{900} ext { taka }}end{array}$

$egin{aligned} herefore ext { For cost price } 100 ext { taka loss } &=frac{36 imes 100}{900} ext { taka } \ &=4 ext { taka } end{aligned}$

Ans: Loss is 4%

(c)

$egin{array}{l}{ ext { As per answer (b) }} \ { ext { Cost price of } 360 ext { bananas is }=900 ext { taka }} \ { herefore ext { cost price of } 1 ext { banana is }=frac{900}{360} ext { taka }}end{array}$

$egin{aligned} herefore ext { Cost price of } 4 ext { bananas is } &=frac{900 imes 4}{360} ext { taka } \ &=10 ext { taka. } end{aligned}$

$egin{array}{l}{ ext { At } 25 \% ext { profit for cost price } 100 ext { taka selling }} { ext { price }=125 ext { taka }}end{array}$

$egin{array}{l}{ herefore ext { For cost price } 1 ext { taka selling price }=frac{125}{100} ext { taka }} \ \ { herefore ext { For cost price } 10 ext { taka selling price }=frac{125 imes 10}{100} mathrm{Tk} ext { . }}end{array}$

$egin{aligned} &=frac{125}{10} ext { taka } \ &=12.5 ext { taka } \ ext { Therefore, for } 25 \% ext { profit businessman should } \ ext { sell bananas at } 12.5 ext { taka per quad (Ans.) } end{aligned}$

20. A principal is turned to an amount in 3 years of Tk. 28,000 and in 5 years of Tk. 30,000 at simple interest.

A. Using the symbols in details, write the formula for Principal.

B. Find out the rate of interest or proﬁts.

C. How much principal should be deposited to get the amount of Tk. 48, 000 at the same rate of interest?

কোনও আসল ৩ বছরের সরল মুনাফাসহ ২৮০০০ টাকা এবং ৫ বছরের সরল মুনাফাসহ ৩০০০০ টাকা।

ক। প্রতীকগুলোর বর্ণনাসহ মূলধন নির্ণয়ের সূত্রটি লিখ।

খ। মুনাফার হার নির্ণয় কর।

গ। একই হারে ব্যাংকে কত টাকা জমা রাখলে ৫ বছরের মুনাফা-আসলে ৪৮০০০ টাকা হবে?

Solution:

(a)

$egin{array}{l}{ ext { Formula to determine principal, }} {mathrm{A}=mathrm{P}(1+mathrm{rn})} \ { ext { Where, }} \ {mathrm{A}= ext { profit principal }} \ {mathrm{r}= ext { rate of profit }} \ {mathrm{n}= ext { number of years }} \ {mathrm{p}= ext { principal }}end{array}$

(b)

$egin{array}{l}{ ext { Let, principal }=p ext { and rate of profit }=r} \ { ext { As per the formula mentioned in answer (a) }} \ { ext { For the first condition of the stem, }} \ {28000=p(1+3 r) ldots ldots ldots ext { (i) }}end{array}$

$egin{array}{l}{ ext { For the second condition of the stem, }} \ {30000=p(1+5 r) ldots ldots ldots ldots(2)} \ { ext { Now, dividing equation }(1) ext { by equation }(2) ext { we }} { ext { get, }}end{array}$

$egin{array}{l}{frac{28000}{30000}=frac{mathrm{P}(1+3 mathrm{r})}{mathrm{P}(1+5 mathrm{r})}} \ \ { ext { or, } frac{14}{15}=frac{1+3 mathrm{r}}{1+5 mathrm{r}}} \ \ { ext { or, } 15+45 mathrm{r}=14+70 mathrm{r}} \ \ { ext { or, } 70r-45 mathrm{r}=15-14} \ { ext { or, } 25 mathrm{r}=1}end{array}$

$egin{array}{l}{ ext { or, } r=frac{1}{25}} \ \ { ext { or, } r=frac{4}{100}} \ \ { herefore r=4 \%} \ \ { ext { Therefore, rate of profit is } 4 \%( ext { Ans. })}end{array}$

(c)

$egin{array}{l}{ ext { From answer ( b ) }} \ \ { ext { Rate of profit, } r=frac{1}{25}} \ \ { ext { Here Number of years, } n=5 ext { years }} \ \ { ext { Profit-principal, } A=48000 ext { taka }} \ \ { ext { Let, principal }=P} \ \ { ext { We know, }} \ {A=P(1+r n)} \ \ { ext { or, } 48000=Pleft(1+frac{1}{25} imes 5 ight)}end{array}$

$egin{array}{l}{ ext { or, } 48000=mathrm{P}left(frac{5+1}{5} ight)} \ \{ ext { or, } 48000=mathrm{P} imes frac{6}{5}} \ \ { ext { or, } mathrm{P}=frac{5 imes 48000}{6}} \ { herefore mathrm{P=40000}} \ { ext { Hence, required principal is } 40000 ext { taka }}end{array}$

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