Kanika was given her pocket money on Jan $ 1^{\text {st }}, 2008 $. She puts Re 1 on Day 1 , Rs 2 on Day 2, Rs 3 on Day 3 , and continued 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?
Given:
Kanika was given her pocket money on Jan \( 1^{\text {st }}, 2008 \). She puts Re 1 on Day 1 , Rs 2 on Day 2, Rs 3 on Day 3 , and continued 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.
To do:
We have to find her pocket money for the month.
Solution:
Let her pocket money for the month be Rs. $x$.
She takes Rs. 1 on day 1, Rs. 2 on day 2, Rs. 3 on day 3 and so on till the end of the month, from this money.
This implies,
Total money taken $=1+2+3+4+\ldots+31$
This forms an AP.
Here,
First term $(a)=1$
Common difference $(d)=2-1=1$
We know that,
Sum of $n$ terms of an AP $S_{n}=\frac{n}{2}[2 a+(n-1) d]$
Sum of the amount taken $=S_{31}$
$S_{31}=\frac{31}{2}[2 \times 1+(31-1) \times 1]$
$=\frac{31}{2}(2+30)$
$=\frac{31 \times 32}{2}$
$=31 \times 16$
$=496$
Therefore,
Kanika takes Rs. 496 till the end of the month from the total money.
She spent Rs. 204 of her pocket money and found that at the end of the month she still has Rs. 100 with her.
This implies,
$(x-496)-204=100$
$x-700=100$
$x= 800$
Hence, her pocket money for the month was Rs. 800.
Related Articles
- Sarika spent $\frac{2}{5}$ of her money on buying skirt. She then spent $\frac{4}{9}$ of her remaining money on a belt. What fraction of her money was left?
- Raveena spends $\frac{1}{3}$ of her scholarship money on books. For buying science magazines she additionally spends $\frac{1}{2}$ of what she spends on books. The remaining amount was spent on tuition. What part of her scholarship money does Raveena spend on tuition fees?
- The monthly pocket money of six friends is given below:Rs. 45, Rs. 30, Rs. 40, Rs. 50, Rs. 25, Rs. 45What is the highest pocket money?
- The monthly pocket money of six friends is given below:Rs. 45, Rs. 30, Rs. 40, Rs. 50, Rs. 25, Rs. 45What is the lowest pocket money?
- The monthly pocket money of six friends is given below:Rs. 45, Rs. 30, Rs. 40, Rs. 50, Rs. 25, Rs. 45Arrange the amounts of pocket money in ascending order.
- Kritika purchased a gift online. She paid the bill amount of Rs. 121.50 online. Now, her bank account has a balance of Rs. 832.25. How much money was there in her account before the purchase?
- Ramkali would need Rs. 1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved Rs. 50 in the first month of this year and increased her monthly saving by Rs. 20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
- If chameli has Rs 600 left after spending 75% of her money. How much, did she have in the beginning.
- In a year, Seema earns $Rs.\ 1,50,000$ and saves $Rs.\ 50,000$. Find the ratio of(a) Money that Seema earns to the money she saves.(b) Money that she saves to the money she spends.
- Aruna has only Re 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75 , then the number of Re 1 and Rs 2 coins are, respectively(A) 35 and 15(B) 35 and 20(C) 15 and 35(D) 25 and 25
- Rani bought tickets for Kashmir for 25 student of her class costing Rs. 624 each and also, she spent ₹25 on an auto rickshaw. What was her total expenditure?
- Sheila spends 15 % of her pocket money on mango juice, one-fifth of it on orange juice, and 5 % in paying fines, what fractional part of the whole has she left?
- The monthly pocket money of six friends is given below:Rs. 45, Rs. 30, Rs. 40, Rs. 50, Rs. 25, Rs. 45What is the range?
- Rani had Rs. 18.50. She bought one ice cream for Rs. 11.75. How much money does she have now?
- Resham wanted to save at least Rs. 6500 for sending her daughter to school next year (after 12 months). She saved Rs. 450 in the first month and raised her savings by Rs. 20 every next month. How much will she be able to save in next 12 months? Will she be able to send her daughter to the school next year?
Kickstart Your Career
Get certified by completing the course
Get Started