Ramkali would need Rs. 1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved Rs. 50 in the first month of this year and increased her monthly saving by Rs. 20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?

Given:

Ramkali would need Rs. 1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved Rs. 50 in the first month of this year and increased her monthly saving by Rs. 20.

To do:

We have to find the amount she saves after a year and whether she will be able to fulfil her dream of sending her daughter to school.

Solution:

Amount saved in the first month $=Rs.\ 50$

Savings raised each successive month $=Rs.\ 20$

Amount saved in each month for 12 months (in Rupees) is,

$50, 70, 90, ......$(12 terms)

This is in A.P., where

First term $a = 50$

Common difference $d = 20$

Number of terms $n = 12$

We know that,

Sum of $n$ terms in an A.P. $S_n = \frac{n}{2}[2a + (n – 1) d]$

$S_n = \frac{12}{2}[2 (50) + (12 – 1) 20]$

$ = 6[100 + 220]$

$= 6(320)$

$=1920$

 Therefore, she will be able to save Rs. 1920 in 12 months which is more than the money required for admission fee, books etc.

Hence, she will be able to fulfil her dream of sending her daughter to school.

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Updated on: 10-Oct-2022

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