Question

Deepak repays his total loan of Rs. 1,00,000 by paying every month, starting with the first instalment of Rs. 10000. If he increases the instalment by Rs.1000 every month, what amount will be paid by him in the 30th instalment​

Answer 1

$\underline{ \bold{ \red{The \: correct \: option \: is:}}}$

$\rightarrow \: { \bold{(A) Rs \: 4900 }}$

$\underline{ \bold{ \red{Explanation: }}}$

$\bullet \: \bold{1st \: instalment = Rs 1000 }$

$\bullet \: { \bold{2nd \: instalment = Rs1000 + Rs 100 = Rs 1100 }}$

$\bullet \: \bold{3rd \: instalment = Rs 1100 + Rs 100 = Rs 1200 </p><p>and so on }$

Let number of instalments

$\rightarrow \: {n .'. 1000 + 1100 + 1200 + ... up \: to \: n \: terms}$

$\: =118000$

$\rightarrow \: n/2[2 x 1000 + (n - 1) 100] = 118000$

$\rightarrow \: 100n2 + 1900n - 236000 = 0$

$\rightarrow \: n2 + 19n - 2360 = 0 => (n + 59)(n - 40) = 0 .'.$

$\bold{Total \: no. \: of \: instalments = 40 }$

$\bold{Now, \: last \: instalment }$

$\: = 40th \: \: instalment . .. a40 = a + 39d$

$\boxed{= Rs 4900}$