Sure, see below my solution to this, and happy to walk you through some tips on how to solve these kind of cases in a dedicated session together!

In the case provided, we have to reason in terms of unitary revenues & margins as we have no info on competitor volume sales. 

So in detail, I would proceed as follows:

Problem 1:

1. Define our client's price ad an arbitrary amount (e.g. 100€). From there we know the competitor's price is 10% less, i.e. 90€.
2. From the case we know our client's margin is 10% (i.e. costs are 90%), therefore unitary costs are 90€. From this we know the competitor's costs are 20% less, i.e. 90€ x (1-20%) = 72€
3. Now we can compute the competitor's absolute unitary margin as 90€ - 72€ = 18€, and in percentage terms as 18€ / 90€ = 20%

Problem 2:

I assume this is a follow up from problem 1. If this is the case, then you know the client's As is cost structure is as follows:

• Raw mat. 70% x 90€ = 63€
• Manufacturing / Autom = 20% x 90€ = 18€
• Personnel 10% x 90€ = 9€

Keep in mind the case asks us to reach a target profitability equal to our competitor's (i.e. 20%) by reducing Raw mat. costs only. In this case we know that in order to reach a target profitability of 20€, assuming  a constant price at 100€, we need costs to add up to 80€ in total. 
This implies reducing overall costs by 10€ from 90€ (as is) to 80€ (to be) by only saving on raw material.

Therefore raw materials need to drop from 63€ to 53€, equal to a -16% reduction in raw material costs.

Here a downloadable excel for clarity, showing all the passages mentioned above. 

Hope this helps!

https://docs.google.com/spreadsheets/d/19VkMXCoi6fsmXq5gkIvMZ3SlHDc8cKsp/edit?usp=sharing&ouid=116051863605479196955&rtpof=true&sd=true