Question

Resham wanted to save at least ₹6500 for sending her daughter to school next year (after 12 months). She saved ₹450 in the first month and raised her savings by ​₹20 every next month. How much will she able to save in next 12 months ? Will she be able to send her daughter to the school next year ?

Answer 1

It is given that Reshma saved ₹450 in the first month and raised her savings by ₹20 every next month.
So, her savings are in an AP, with the first term (a) = ₹450 and the common difference (d) = ₹20.
We need to find her savings for 12 months, so n = 12.
We know that the sum of n terms of an AP is $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$.
Reshma's savings for 12 months:
$$\begin{gathered} S_{12}=\frac{12}{2}\left[2\times 450+\left(12-1\right)\times 20\right] \\ =6\left(900+220\right) \\ =6\times 1120 \\ =6720 \end{gathered}$$
So, she will save ₹6,720 in 12 months.
She needed to save at least ₹6,500 for sending her daughter to school next year.
Since ₹6,720 is greater than ₹6,500, Reshma can send her daughter to school.
The question aims to encourage personal savings and emphasise the need of female education.