Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000
Solution:
Given, Yasmeen saves Rs 32 in the first month, Rs 36 in the second month and Rs 40 in the third month.
We have to find how many months it will take to save in this manner upto Rs 2000.
The series is 32, 36, 40,.....
Common difference, d = 36 - 32 = 4
First term, a = 32
Sum = 2000
The sum of the first n terms of an AP is given by
Sₙ = n/2[2a + (n-1)d]
So, 2000 = n/2[2(32) + (n - 1)(4)]
2000 = n/2[64 + 4n - 4]
4000 = n[4n + 60]
4n² + 60n = 4000
4n² + 60n - 4000 = 0
Dividing by 4,
n² + 15n - 1000 = 0
On factoring,
n² + 40n - 25n - 1000 = 0
n(n + 40) - 25(n + 40) = 0
(n - 25)(n + 40) = 0
Now, n - 25 = 0
n = 25
Also, n + 40 = 0
n = -40
Since a negative value is not possible, n = -40 is neglected.
Therefore, the number of months required to save upto Rs.2000 is 25.
✦ Try This: Meenu saves Rs 28 during the first month, Rs 35 in the second month and Rs 42 in the third month. If she continues to save in this manner, in how many months will she save Rs 700
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 35
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000
Summary:
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, she will save Rs 2000 in 25 months.
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