Question

Poonam saved Rs. 5 in the first week of the year and then increased her weekly savings by Rs. 1.75 each week. In which week will her weekly savings be Rs. 20.75?

Answer 1

Hint: We solve this problem by using the arithmetic progression. The general representation of arithmetic progression is
 \[a,a+d,a+2d,..............\] Where, \['a'\] is the first term and \['d'\] is a common difference.
For this progression the \[{{n}^{th}}\] term is given as
 \[{{T}_{n}}=a+\left( n-1 \right)d\]
By using this formula we calculate the required week.

Complete step by step answer:
We are given that Poonam saves 5/- in the first week of a year.
We are given that she increases her savings by 1.75/- every week.
Based on this information let us build a arithmetic progression as follows
 \[5,5+1.75,5+2\left( 1.75 \right),......\]
Here, we can take that ‘5’ as the first term of the progression and ‘1.75’ as the common difference of the arithmetic progression.
We know that if the arithmetic progression is
 \[a,a+d,a+2d,..............\] Where, \['a'\] is first term and \['d'\] is common difference then the \[{{n}^{th}}\] term is given as
 \[{{T}_{n}}=a+\left( n-1 \right)d\]
By applying the this formula to above build up progression we get
 \[\begin{align}
  & \Rightarrow {{T}_{n}}=a+\left( n-1 \right)d \\
 & \Rightarrow {{T}_{n}}=5+\left( n-1 \right)1.75......equation(i) \\
\end{align}\]
We are asked to find in which week her savings will be 20.75/-.
So, the \[{{n}^{th}}\] term of our build up progression is 20.75.
 \[\Rightarrow {{T}_{n}}=20.75.......equation(ii)\]
Now, by combining equation (i) and equation (ii) we get
 \[\begin{align}
  & \Rightarrow 20.75=5+\left( n-1 \right)1.75 \\
 & \Rightarrow n-1=\dfrac{15.75}{1.75} \\
 & \Rightarrow n=9+1=10 \\
\end{align}\]
Therefore, we can say that by the \[{{10}^{th}}\] week of the year Poonam will make her savings to Rs. 20.75.

So, the correct answer is “10”.

Note: Students may make mistakes in understanding the question that is we are asked to find in which week the savings will be Rs. 2075. So, we need to make this 20.75 as \[{{n}^{th}}\] term not the sum of \['n'\] terms. If the question is asked to find how many weeks it takes to collect Rs. 20.75 then we should make 20.75 as sum of \['n'\] terms.