A	:	B	:	C
	3	:	4	:	5
Let	3x	:	4x	:	5x

∴ Sum of (smallest + largest) A + C = 8x According of the question, 8x = 4x + 52 4x = 52 ∴ Smallest number is = A ⇒ 13 $\times$ 3 = 39

A + B = 40

A - B = 4

∴ A = 22

B = 18

A : B = 22 : 18

= 11 : 9

\begin{align} & {\text{Let the fourth proportional to}} \cr & \left( {{a^2} - {b^2}} \right), \left( {{a^2} - ab} \right), \left( {{a^3} + {b^3}} \right)\, {\text{be}}\, x. \cr & {\text{Then, }} \cr & = \left( {{a^2} - {b^2}} \right):\left( {{a^2} - ab} \right)::\left( {{a^3} + {b^3}} \right):x \cr & \Rightarrow \left( {{a^2} - {b^2}} \right)x = \left( {{a^3} + {b^3}} \right)\left( {{a^2} - ab} \right) \cr & \Rightarrow x = \frac{{\left( {{a^3} + {b^3}} \right)\left( {{a^2} - ab} \right)}}{{\left( {{a^2} - {b^2}} \right)}} \cr & \, \, \, \, \, \, \, = \frac{{\left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)a\left( {a - b} \right)}}{{\left( {a - b} \right)\left( {a + b} \right)}} \cr & \Rightarrow x = a\left( {{a^2} - ab + b} \right). \cr\end{align}

Let,

B₁ : B₂ : B₃ = 3x : 4x : 5x

Again,

B₁ : B₂ : B₃ = 5y : 4y : 3y

Number of oranges remain constant in third basket as increase in oranges takes place only in first two baskets.

Hence, 5x = 3y

and,

3x : 4x : 5x

→^9y/₅ : ^12y/₅ : ^15y/₅ = 9y : 12y : 15y

And,

5y : 4y : 3y → 25y : 20y : 15y

Therefore, Increment in first basket = 16.

Increment in second basket = 8.

Thus, Required ratio = 16 /8 = 2 : 1

The total number of members must be a multiple of the sum ratio terms.

3 + 2 = 5

and 25 is a multiple of 5