Peter, James and David shared some money in the ratio Peter:James = 2:3 and James:David = 4:5. If David received Ksh. 35,250, find Peter's share.

James : David.
Given ratios:
Peter : James = $2:3$
James : David = $4:5$

To combine these, we need to make the 'James' part of the ratio the same. The least common multiple of 3 and 4 is 12.
Multiply the first ratio by 4:
Peter : James = $(2 \times 4) : (3 \times 4) = 8:12$
Multiply the second ratio by 3:
James : David = $(4 \times 3) : (5 \times 3) = 12:15$

Now, the combined ratio Peter : James : David is $8:12:15$.

Total parts = $8 + 12 + 15 = 35$ parts.

The total contribution is Ksh. 82,250.
Value per part = $\frac{\text{Total contribution}}{\text{Total parts}}$

David's share in the ratio is 15 parts.
David's contribution = David's parts $\times$ Value per part

David contributed $\text{Ksh. } 35,250$.