If $x+y=a{x}^2+y^2=b^2$ and $x^3+y^3=c^3$ then show that $a^3+2c^3=3a{b}^2$

On selling a chair at 7% loss and a table at 17% gain, a man gains Tk 296. If he sells the chair at 7% gain and the table at 12% gain, then he gains Tk. 400. The actual price of the table and Chair is-

Here, Applying Loss/Gain Adjustment,

(17+12)% = 696 Tk.

So, 100% = 2400 Tk.

Again, -7%+17% of 2400=296 Tk.

So, 7% =112

So, The Actual Price of Table and Chair is 2400 Tk. and 1600 Tk. respectively (Ans)

Here, Let the diagonal of the Rhombus is d₁ and d₂

Atq, $\frac{1}{2}\times d_1\times d_2=120$

So, $d_2=120\times \frac{2}{10}$= 24 meter

So, One Side of the Rhombus is 13 [As half of each diagonal is 5 and 12 which is Pythagorian Triplet]

So, Perimeter of The Rhombus = 13 $\times$ 4 = 52 meter (Ans)

Let, The Rate of Interest ber Tk.

Atq, $500\times 4\times \frac{r}{100}+600\times 5\times \frac{r}{100}=500$

So, 20r + 30r = 500

So, r = 10

So, Required Amount of Interest $=1000\times 3\times \frac{10}{100}$ = 300Tk . (Ans)