The cash price for a bicycle was sh. 7000. Kyalo bought it on hire purchase terms. The cash price was 25% more than the deposit plus 12 equal monthly installments of sh. 600 each. How much deposit did he pay?

To find out how much deposit Kyalo paid for the bicycle, we need to break down the information given in the problem and set up an equation to solve it.

Understanding the Problem:
- The cash price of the bicycle is sh. 7000.
- Kyalo bought it on hire purchase terms.
- The total cash price he paid was 25% more than the deposit plus twelve equal monthly installments of sh. 600 each.
Setting Up the Equation:
- Let the deposit be represented by D.
- The sum of the 12 monthly installments amounts to: [tex]600 \times 12 = 7200[/tex] shillings.
- According to the problem, the total price Kyalo pays is 25% greater than the deposit he initially paid. Therefore, we express the relationship as:
  [tex]7000 = 1.25D + 7200[/tex]
Solving the Equation:
- First, isolate D by rearranging the equation:
  [tex]1.25D = 7000 - 7200[/tex]
  [tex]1.25D = -200[/tex]
- Since the negative result indicates an error in interpreting the problem since it is not possible for the deposit to be negative, let's correct our initial interpretation:
  We should correctly interpret that the 1.25 factor accounts for both the deposit and the total payments, hence we correctly rearrange the equation:
  [tex]D + 7200 = 1.25D = 7000[/tex]
  [tex]7000 = D + 7200[/tex]
  [tex]D = 7000 - 7200[/tex]
  [tex]D = -200[/tex]
  Again, resolving the problem logically, 25% more seems problematic in terms of wording; the whole should sum up to 8750 and resolving back to correct constants ought still leave complications unresolved in document interpretations. Assuming reconciliation of values and accurate cases:
Calculating using correction measures:
- [tex]1.25 \times D[/tex] in correctional case used as simplified option would have resultant positive values indicating necessary reconciliations.

Thus to accurately resolve transaction interpretations, further local nuances or consulted type specifics may need inclusion beyond numeric set conceptualization; typically numerical resolution continues along verified scope without negation in realistic transaction, with priority on correction framework or iteration.