Question

Saving money is a good habit and it should be inculcated in children right from the beginning. Rehan's mother brought a piggy bank for Rehan and put one ₹ 5 coin of her savings in the piggy bank on the first day. She increases his savings by one ₹ 5 coin daily.

Based on the above information, answer the following questions:

1. How many coins were added to the piggy bank on 8^th day? (1)
2. How much money will be there in the piggy bank after 8 days? (1)
3. 1. If the piggy bank can hold one hundred twenty ₹ 5 coins in all, find the number of days she can contribute to put ₹ 5 coins into it. (2)
      OR
      
   2. Find the total money saved when the piggy bank is full. (2)
      

Answer 1

Given:

Saving are increased by one ₹ 5 coin daily

So, Rehan's mother input = 5, 10, 15,...

Number of coins on each day = 1, 2, 3, 4,...

Here AP is formed So, a = 1, d = 1

(i) As the number of coins is increasing by One daily.

So number of coins added on 8^th day = 8.

(ii) As one ₹ 5 coin is added daily money after

8 days ⇒ S₈ = `"n"/2  [2"a" + ("n" - 1) "d"]`

= `8/2  [2 xx 1 + (8 - 1) 1]`

= `4 [2 + 7]`

= 36

Total money in 8 days = 36 × 5

= ₹ 180

(iii) (a)  Number of coins Piggy bank can hold

= 120

∴ S_n ≤ 120

where S_n = `"n"/2  [2"a" + ("n"- 1)"d"]`

⇒ `"S"_"n" = "n"/2  [2 xx 1 + ("n" - 1)1]`

⇒ `"n"/2  [2 + ("n"- 1)] = 120`

⇒ `"n"/2  [2 + "n"- 1] = 120`

⇒ `"n"/2  [1 + "n"] = 120`

= `"n"/2 + "n"^2/2 = 120`

= n² + n = 240

= n² + n − 240 = 0

= n² + 16n − 15n − 240 = 0

= n(n + 16) − 15(n + 16) = 0

= (n + 16)(n − 15) = 0

⇒ n = − 16 and n = 15

Therefore, she can put in coins for 15 days.

OR

(iii) (b) For Amount 5, 10, 15,...

AP = 5, 10, 15,...

⇒ a = 5 and d = 5, n = 15.

`"S"_"n" = "n"/2  [2"a" + ("n" - 1)"d"]`

`"S"_"n" = 15/2  [2 xx 5 + (15 - 1)5]`

`= 15/2 [10 + 70]`

`= 15/2 xx 80`

= ₹ 600

∴ Total money solved = ₹ 600