Ashifur August 8, 2023 - 19:41
Problem: A book and a pen were sold for Tk 3,040 making a profit of 25% on the book and 10% on the pen. By selling them for Tk 3,070; the profit realized would have been 10% on the book and 25% on the pen. Find the cost price of each.

View all: SOUTHEAST BANK (PO) | WRITTEN QUESTION (MATH) SOLVE | 2016

Correct Answer: ans: The cost price of book and pen is 1200 & 1400 Tk. respectively.

Explanation:

Let, cost price of book is Tk x

& Cost price of pen is Tk. y

At, 25% profit the selling price of book will be = (x + x $\times$25%) Tk.

= $x+\frac{25x}{100}=\frac{5x}{4}$ TK

At, 10% profit on pen, the cost price of pen will be = (y + y x 10%) Tk.

= (Y+$\frac{10y}{100}$) = $\frac{11y}{10}$ TK

According to question, $\frac{5x}{4}$ + $\frac{11y}{10}$

=> 25x + 22y = 60,800 …………………………….(i)

In the same way we can form another equation as below

$\frac{11x}{10}$ + $\frac{5y}{4}$ = 3,070

=> $\frac{22x+25y}{20}$ = 3,070

=> 22x+25y = 61,400………………………….(ii)

Subtracting equation (i) from (ii) we will get

550x + 625y = 1535000 [Multiplying by 25]

550x + 484y = 1337600 |Multiplying by 22|

141y = 197400

y = 1400

Putting y = 1400, in equation (i) we get

25x + 22 x 1400 = 60800

=> 25x = 60800 – 30800

=> 25x = 30000

x = 1200

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