Question:medium

A tea shop offers tea in cups of three different sizes. The product of the prices, in INR, of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by INR 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes, in INR, is

Updated On: Jan 15, 2026
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Correct Answer: 40

Solution and Explanation

Rhombus Area Calculation

The area of a rhombus is determined by the formula:

Area = $\dfrac{1}{2} \times d_1 \times d_2$

where $d_1$ and $d_2$ represent the lengths of the rhombus's diagonals.

Step 1: Apply the Area Formula

Given: Area = 96 cm²

$\dfrac{1}{2} \times d_1 \times d_2 = 96$

Multiplying both sides by 2 yields:
$d_1 \times d_2 = 192$

Step 2: Relate Diagonals to the Side Length

The diagonals of a rhombus bisect each other perpendicularly. Therefore, 
$\left(\dfrac{d_1}{2}\right)^2 + \left(\dfrac{d_2}{2}\right)^2 = 10^2$

This simplifies to: 
$\Rightarrow \dfrac{d_1^2}{4} + \dfrac{d_2^2}{4} = 100$

Multiplying both sides by 4 results in: 
$d_1^2 + d_2^2 = 400$

Step 3: Utilize Algebraic Identity

The identity used is: $(d_1 + d_2)^2 = d_1^2 + d_2^2 + 2d_1d_2$

Substituting the known values: 
$(d_1 + d_2)^2 = 400 + 2 \times 192 = 400 + 384 = 784$

Taking the square root of both sides gives: 
$\Rightarrow d_1 + d_2 = \sqrt{784} = 28$

Step 4: Determine Wiring Cost

The total length of wire needed for both diagonals is $d_1 + d_2 = 28$ meters.

The cost per meter is ₹125. 
The total cost is calculated as: $28 \times 125 = ₹3500$

Final Result:

₹3500

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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
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