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10th Class Mathematics Arithmetic Progressions Question Bank Arithmetic Progressions

  • question_answer
    Raghav buys a shop for Rs. 120000. He pays half of the amount in cash and agrees to pay the balance in 12 annual instalments of Rs. 5000 each. If the rate of interest Is 12% and he pays the interest due on the unpaid amount with the instalment. Find the total cost of the shop.

    A) Rs.156800                  

    B) Rs.156700      

    C)        Rs.165200       

    D)         Rs.166800                 

    Correct Answer: D

    Solution :

    Amount paid in cash \[=Rs.\left( \frac{1}{2}\times 120000 \right)=Rs.\,\,60000\] Remaining amount \[=\text{ Rs}\text{.(}120000-60000)\text{ =Rs}\text{. }60000\]Amount of 1st instalment \[=Rs.(5000+\frac{12}{100}\times 60000)=Rs.\,12200\] Amount of 2nd instalment \[=Rs.(5000+\frac{12}{100}\times 55000)=Rs.\,11,600\] Amount of 3rd instalment \[=Rs.\,\left( 5000+\frac{12}{100}\times 50000 \right)=Rs.\,11,000\] Total amount paid \[=Rs.12200+Rs.11600+Rs.11000\]+... (12 instalments) which form an A.P. with number of terms, \[n=12,\text{ }a=12200\]and \[d=-600\] \[\therefore \]   Sum  \[=n\frac{n}{2}\left[ 2a+(n-1)d \right]\] \[=\frac{12}{2}\left[ 2\times 12200+11\times \left( -600 \right) \right]=106800\] \[\therefore \]  Total cost of the shop \[=Rs.60000+Rs.106800=Rs.166800\]


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