in this question why can't we solve the equations we get from sum of 40 instalments and sum of 10 instalments-Q-A man arranges to pay a debt off rs 3600 by 40 annual instalments which form an AP.when 30 instalments are paid ,he dies leaving one-third of the debt unpaid,find the value of first instalment.ANSWER IS RS 51, NO LINKS PLZ

Dear Student,

Please find below the solution to the asked query:

From given information we know :

S₄₀ =  3600 

And

S₃₀ = 3600 - $\frac{1}{3}\times 3600$ =  3600 -  1200 =  2400

We know sum of n terms of A.P. :

S_n =  $\frac{n}{2}\left[ 2a + \left( n - 1 \right)d \right]$ , So

$$\begin{gathered} \frac{40}{2}\left[ 2a + \left( 40 - 1 \right) d \right] = 3600 \\ \Rightarrow 20\left[ 2a + 39 d \right] = 3600 \\ \Rightarrow 2a + 39 d= 180 --- ( 1\hspace{0.17em}) \end{gathered}$$

And

$$\begin{gathered} \frac{30}{2}\left[ 2a + \left( 30 - 1 \right) d \right] = 2400 \\ \Rightarrow 15\left[ 2a + 29 d \right] = 2400 \\ \Rightarrow 2a + 29 d= 160 --- ( 2\hspace{0.17em}) \end{gathered}$$

Now we subtract equation 2 from equation 1 and get

10 d  =  20

d  = 2 , Substitute that value in equation 1 and get

2 a + 39 ( 2 ) =  180

2 a + 78 = 180

2 a = 102

a  = 51

Therefore ,

Value of first instalment =  Rs . 51                                                               ( Ans )


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