I Don't get the solution. I need an explanation or Is there any videos on you tube to understand

Question

A man buys 20 pens and 12 books for tk 400.He sells pens at a profit of 40% and books at a gain of 25%.If his overall profit was to 112.The cost price of the book is?detail pls Ans

40%400 - 112 = 48 (40-25) i.e. 15% of 32 B = 48 So, B = 48100/(15*32) = 10

Answer 1

Let $b$ be the cost of a book, and let $p$ be the cost of a pen. From the first statement in the problem, we must have:

$$20p + 12b = 400$$

Now, since the man sells the pens for $1.4$ times their price, and sells books for $1.25$ times their price, making a profit of $112$, we find:

$$1.4\cdot 20p + 1.25\cdot 12b = 400 + 112$$

We find the system of equations:

$$20p + 12b = 400$$

$$28p + 15b = 512$$

Can you take it from here?

If you're still stuck:

Multiplying the first equation by $5$ and the second by $4$: $$100p + 60b = 2000$$ $$112p + 60b = 2048$$ Subtracting the first equation from the second: $$12p = 48$$ $$p = 4$$ Substituting into the original cost equation: $$80 + 12b = 400$$ $$12b = 320$$ $$b = \frac{80}{3}$$ Thus: $$\boxed{\text{A book costs approximately }26.67}$$

Answer 2

Your book's answer is wrong. I get the cost price of a book to be $\frac{80}3$ and that of a pen to be $4$ in whatever currency you're using. These numbers check out when substituted back into the conditions of the problem statement.

Let the cost price of a single book be $b$. Then the cost price of a single pen is $\frac{400 - 12b}{20}$. The total cost (outlay) is $400$. The total selling price (revenue) is $1.4 \times 20 \times \frac{400 - 12b}{20} + 1.25 \times 12 \times b = 560 - 1.8b$.

The difference between selling price and cost is the profit, so we form the equation $560-1.8b - 400 = 112$, the solution of which is $b = \frac{80}3$.