In a tin of baked beans, weight of beans : weight of tomatoes : weight of other ingredients = 6: 3: 1 was there are 150 g of tomatoes in the tin work out the weight of the beans

Step-by-step

When dealing with ratios, we can multiply or divide at will (but not add or subtract).  The present question gives a good example:

Given:

Tomatoes = 150 g.

Beans : tomatoes : others  =  6:3:1

Solution:

We note that there are 150g of tomatoes, and the ratio of tomatoes is 3.

We can therefore multiply the ratio by 150/3 = 50 to get the true weight of all ingredients (as long as tomatoes correspond to the true weight)

Beans : tomatoes : others

= 6:3:1      [ multiply by 150/3=50]

=300:150:50

So

beans weigh 300 g

tomatoes 150 g

others weight 50 g.