Question

If Books and More have earned 20% profit overall, then in film DVDs they made:

• A. 15.2% profit
• B. 10.0% profit
• C. 10.0% loss
• D. 16.3% loss
• E. 23.4% loss
• A. 12.3% profit
• B. 8.7% profit
• C. 0.4% loss
• D. 6.25% loss
• J. None of these
• A. 15
• B. $15\sqrt{3}$
• C. 16
• D. $16\sqrt{3}$
• O. None of the above

Answer 1

The Correct Option is B

Step 1: Assume cost price base.
Let total cost price of all items (books, CDs, DVDs) = ₹ 100x.
Given overall profit = 20%, so total selling price =
\[ \text{S.P.}_{\text{total}} = 120x \] Step 2: Split into contributions.
It is given CDs contribute 35% of total sales. \[ \text{S.P.}_{\text{CD}} = 0.35 \times 120x = 42x \] Also, sales from books = 50% more than CDs = $42x \times 1.5 = 63x$. So, \[ \text{S.P.}_{\text{books}} = 63x, \quad \text{S.P.}_{\text{DVDs}} = 120x - (42x+63x) = 15x \] Step 3: Compute cost prices of CDs and books.
- CDs: 40% profit $\Rightarrow$ C.P. = $\frac{100}{140}\times 42x = 30x$.
- Books: 25% profit $\Rightarrow$ C.P. = $\frac{100}{125}\times 63x = 50.4x$.
Step 4: Deduce cost price of DVDs.
Total C.P. = $100x$. So, \[ \text{C.P.}_{\text{DVDs}} = 100x - (30x+50.4x) = 19.6x \] Step 5: Compute loss on DVDs.
Loss = C.P. – S.P. = $19.6x - 15x = 4.6x$.
Loss% = $\dfrac{4.6x}{19.6x}\times 100 = 23.47% \approx 23.4%$.
Final Answer: \[ \boxed{23.4% \ \text{loss}} \]

Answer 2

Step 1: Assume total selling price base.
Let total S.P. = ₹ 100x.
Step 2: Divide into components.
- S.P. of CDs = 35% of 100x = $35x$.
- S.P. of books = 1.5 times CDs = $1.5 \times 35x = 52.5x$.
- S.P. of DVDs = remaining = $100x - (35x+52.5x) = 12.5x$.
Step 3: Find cost prices of CDs and books.
- CDs: 40% profit $\Rightarrow$ C.P. = $\tfrac{100}{140}\times 35x = 25x$.
- Books: 25% profit $\Rightarrow$ C.P. = $\tfrac{100}{125}\times 52.5x = 42x$.
Step 4: DVDs loss condition.
Given 50% loss on DVDs.
So C.P. of DVDs = $\tfrac{100}{50}\times 12.5x = 25x$.
Step 5: Total cost price and overall profit.
Total C.P. = $25x+42x+25x=92x$.
Total S.P. = $100x$.
Profit = $100x-92x=8x$.
Profit% = $\dfrac{8}{92}\times 100 \approx 8.7%$.
Final Answer: \[ \boxed{8.7% \ \text{profit}} \]

Answer 3

Step 1: Represent sides.
Let sides of parallelogram be $AB = a$ and $BC = b$.
So, area of parallelogram: \[ \text{Area} = ab \sin 60^\circ = \frac{\sqrt{3}}{2} ab \] It is given that area = $\tfrac{15\sqrt{3}}{2}$, hence \[ \frac{\sqrt{3}}{2} ab = \frac{15\sqrt{3}}{2} \quad \Rightarrow \quad ab = 15 \] Step 2: Use cosine rule on diagonal.
Diagonal $AC$ or $BD$ is the longer diagonal. It is given as $7$.
We know $\triangle ABD$ has $\angle ABD = 120^\circ$ (since $\angle ABC = 60^\circ$, adjacent interior angle = $180^\circ - 60^\circ = 120^\circ$).
By cosine rule in $\triangle ABD$: \[ AD^2 + AB^2 - 2(AB)(AD)\cos 120^\circ = BD^2 \] That is, \[ a^2 + b^2 - 2ab \times \Big(-\frac{1}{2}\Big) = 7^2 \] \[ a^2 + b^2 + ab = 49 \] Since $ab=15$, \[ a^2 + b^2 = 49 - 15 = 34 \] Step 3: Compute $(a+b)^2$.
\[ (a+b)^2 = a^2+b^2+2ab = 34 + 2(15) = 34 + 30 = 64 \] So, \[ a+b = \sqrt{64} = 8 \] Step 4: Perimeter of parallelogram.
Perimeter = $2(a+b) = 2 \times 8 = 16$ cm. Final Answer: \[ \boxed{16 \ \text{cm}} \]