Seema has joined a new Company after the completion of her B.Tech

Seema has joined a new Company after the completion of her B.Tech from a reputed engineering college in Chennai. She saves 10% of her income in each of the first three months of her service and for every subsequent month, her savings are Rs. 50 more than the savings of the immediate previous month. If her joining income was Rs. 3000, her total savings from the start of the service will be Rs. 11400 in

  1. 6 months
  2. 12 months
  3. 18 months
  4. 24 months

Solution

Savings in first three months = Rs. 900

Remaining savings = Rs.11400 - Rs.900 = Rs.10500

Let number of more months to save remaining amount be x.

350 + 400 + ... + x terms = 10500

7 + 8 + ... + x terms = 210

210 = x/2[2×7 + (x-1)]

420 = 13x + x2

x2 + 13x - 420 = 0

x = 15

So, in 15 + 3 = 18 months her savings will be Rs. 11,400.

The correct option is C.