A man saves 200 in each of the first three months of his service.

Question

A man saves 200 in each of the first three months of his service. In each of the subsequent months his saving increases by 40 more than the saving of the immediately previous month. His total saving from the start of service will be 11040 after:

Accepted Answer

Let required number of months $=n$

$$\therefore$$ $$200 \times 3 + \left( {240 + 280 + 320 + ...} \right.$$

$$\left. {\,\,\,\,\,\,\,\,\,\,\,\, + {{\left( {n - 3} \right)}^{th}}\,term} \right) = 11040$$

$$ \Rightarrow {{n - 3} \over 2}\left[ {2 \times 240 + \left( {n - 4} \right) \times 40} \right]$$

$$\,\,\,\,\,\,\,\,\,\,\,\, = 11040 - 600$$

$$ \Rightarrow \left( {n - 3} \right)\left[ {240 + 20n - 80} \right] = 10440$$

$$ \Rightarrow \left( {n - 3} \right)\left( {20n + 160} \right) = 10440$$

$$ \Rightarrow \left( {n - 3} \right)\left( {n + 8} \right) = 522$$

$$ \Rightarrow {n^2} + 5n - 546 = 0$$

$$ \Rightarrow \left( {n + 26} \right)\left( {n - 21} \right) = 0$$

$$\therefore$$ $n = 21$

Solutions · 1