Resham wanted to save at least Rs. 6500 for sending her daughter to school next year (after 12 months). 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?

Given:

Resham wanted to save at least Rs. 6500 for sending her daughter to school next year (after 12 months). She saved Rs. 450 in the first month and raised her savings by Rs. 20 every next month.

To do:

We have to find the amount she saves in the next 12 months and whether she will be able to send her daughter to the school next year.
Solution:

Amount saved in the first month $=Rs.\ 450$

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

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

$450, 470, 490, ......$(12 terms)

This is in A.P., where

First term $a = 450$

Common difference $d = 20$

Number of terms $n = 12$

We know that,

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

$S_n = \frac{12}{2}[2 (450) + (12 – 1) 20]$

$ = 6[900 + 220]$

$= 6(1120)$

$=6720$

Therefore, Resham saves Rs. 6720 in next 12 months which is more than the amount required for sending her daughter to school.

Hence, Resham will be able to send her daughter to school.

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Simply Easy Learning

Updated on: 10-Oct-2022

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