Kanika was given her pocket money on Jan 1st, 2008. She puts Re 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continues doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month
Solution:
It is stated that Kanika was given pocket money on Jan 1st 2008.
She put Re.1 on day 1, Rs.2 on day 2, Rs.3 on day, and so on into her piggy bank till the end of the month.
We have to find the amount of pocket money for the month.
January has 31 days.
So, the series will be 1, 2, 3, ……….,31.
From the series,
First term, a = 1
Last term, l = 31
Common difference, d = 2 -1 = 1
If l is the last term of an AP, then the sum of the terms is given by
S = n/2[a+l]
Here, n = 31
So, S = 31/2[1 + 31]
= 31/2[32]
= 31(16)
S = 496
Given, Rs. 204 from the pocket money was spent by Kanika.
After spending the amount of money left in the piggy bank is Rs.100.
Kanika’s total pocket money = 496 + 204 + 100
= 496 + 304
= 800
Therefore, the total pocket money is Rs.800.
✦ Try This: Asha was given her pocket money on Feb 1st, 2008. She puts Re 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continues doing so till the end of the month, from this money into her piggy bank. She also spent Rs 50 of her pocket money, and found that at the end of the month she still had Rs 90 with her. How much was her pocket money for the month
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 34
Kanika was given her pocket money on Jan 1st, 2008. She puts Re 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continues doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month
Summary:
Kanika was given her pocket money on Jan 1st, 2008. She puts Re 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continues doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. Her pocket money for the month was Rs.800
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