Given:
- Ratio of gold and silver in first alloy = 1:2
- Ratio of gold and silver in second alloy = 2:3
- Ratio of gold and silver in the new alloy = 3:5

To find:
- Parts of the two alloys needed to obtain the new alloy

Solution:
Let's assume that x parts of the first alloy and y parts of the second alloy are taken to form the new alloy.

Gold ratio in first alloy = 1/(1+2) = 1/3
Silver ratio in first alloy = 2/(1+2) = 2/3

Gold ratio in second alloy = 2/(2+3) = 2/5
Silver ratio in second alloy = 3/(2+3) = 3/5

Gold ratio in new alloy = 3/(3+5) = 3/8
Silver ratio in new alloy = 5/(3+5) = 5/8

We need to find x and y such that the ratio of gold and silver in the new alloy is 3:5.

- Gold in new alloy = (x*1/3) + (y*2/5) = (3/8)*(x+y)
- Silver in new alloy = (x*2/3) + (y*3/5) = (5/8)*(x+y)

We can solve these two equations to get the values of x and y.

Multiplying the first equation by 15 and the second equation by 24, we get:

- 5x + 6y = 9(x+y)
- 8x + 18y = 15(x+y)

Simplifying these equations, we get:

- 4x - 3y = 0
- 3x - 6y = 0

Solving these equations, we get:

x = 3y/2

Substituting this value of x in the first equation, we get:

5y = 24(x+y)/8

Simplifying this equation, we get:

y = 5

Substituting this value of y in the equation x = 3y/2, we get:

x = 7.5

Therefore, the parts of the two alloys needed to obtain the new alloy are 7.5 and 5.

Answer:
Option (B) 3 and 5.