Question

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

Answer 1

Let a be the first term and d be the common difference.
We know that, sum of first n terms = S_n = \[\frac{n}{2}\][2a + (n − 1)d]

According to the question,
Saving of Ramkali in 1 year = ₹50 + ₹70 + ₹90.......

Here, a = 50, d = 70 − 50 = 20 and n = 12.

∴ S₁₂ = \[\frac{12}{2}\][2 × 50 + (12 − 1)20]
          = 6[100 + 220]
          = 6 × 320
         = 1920

Hence, After a year, she will save ₹1920.

Since, required amount for admission is ₹1800 and her savings will be ₹1920.

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