Question

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

Answer 1

Correct Answer: 40

Area of the Rhombus 

The area of a rhombus is given by:

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

where $d_1$ and $d_2$ are the diagonals of the rhombus.

Step 1: Use the Area Formula

Given: Area = 96 cm²

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

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

Step 2: Use Diagonal Relationship with Side

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

$\Rightarrow \dfrac{d_1^2}{4} + \dfrac{d_2^2}{4} = 100$

Multiply both sides by 4: 
$d_1^2 + d_2^2 = 400$

Step 3: Use Identity

$(d_1 + d_2)^2 = d_1^2 + d_2^2 + 2d_1d_2$

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

$\Rightarrow d_1 + d_2 = \sqrt{784} = 28$

Step 4: Calculate Cost of Wiring

Total length of wire required along both diagonals = $d_1 + d_2 = 28$ meters

Cost per meter = ₹125 
Total Cost = $28 \times 125 = ₹3500$

Final Answer:

₹3500