Permutations and Combinations

Permutations and Combinations

Question

Shamshad Ali buys a scooter for Rs 22000. He pays Rs. 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him? 

Answer

Original cost of scooter =  Rs. 22000
Amount paid in cash     =  Rs. 4000
Amount to be paid in instalments =  Rs. 18000
Let a denote the first instalment
                                 a = 1000 + 10% interest on unpaid amount
                                    =  Rs .left square bracket 1000 space plus space 10 over 100 cross times 18000 right square bracket space equals space Rs. space left square bracket 1000 space plus space 1800 right square bracket space equals space Rs. space 2800
rightwards double arrow                             a = Rs. 2800

      2nd instalment = space space 1000 space plus space 10 over 100 cross times 17000 space equals space 1000 plus 1700 space equals space space Rs. space 2700
   Similarly, 3rd instalment  = Rs. 2600
∴  Various instalments are Rs. 2800, Rs. 2700, Rs. 2600.........
Amount paid in instalments = Rs. 2800 + Rs . 2700 + Rs . 2600 + ......+ Rs. 1100
                                    = Rs . space space 18 over 2 left square bracket 2 left parenthesis 2800 right parenthesis space plus space left parenthesis 18 minus 1 right parenthesis left parenthesis negative 100 right parenthesis right square bracket

                                                                  open square brackets table row cell because space space space space space space space a equals space 2800 comma space d space equals space 2700 space minus 2800 space equals space minus 100 comma end cell row cell U sin g space S subscript n space equals space n over 2 left square bracket 2 a plus left parenthesis n minus 1 right parenthesis d end cell end table close square brackets
                                    = Rs. 9[5600 - 1700] = Rs. 9(3900) = Rs. 35100
Actual amount by Hari       = Rs. [35100 + 4000] = Rs 39100

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