Question

Reshma wanted to save at least Rs 6,500 for sending her daughter to school next year (after 12 month.) She saved Rs 450 in the first month and raised her savings by Rs 20 every next month. How much will she be able to save in next 12 months? Will she be able to send her daughter to the school next year?
What value is reflected in this question ?

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:

\[S_{12} = \frac{12}{2}\left[ 2 \times 450 + \left( 12 - 1 \right) \times 20 \right]\]
\[ = 6\left( 900 + 220 \right)\]
\[ = 6 \times 1120\]
\[ = 6720\]

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.