At the time our mother left this Earth, she gave Rs 90000 to her children of birth. This we kept and each year added Rs 30000 more, as a lasting memorial from the children she bore. When Rs 4,20,000 thusly attained, all goes to charity that her memory be maintained. (i) What was the balance in the seventh year? (ii) In what year was the goal of Rs 420,000 met?

Answers 2

Answer:

1) 2,10,000

2) 3years 6months = 3.5years

Step-by-step explanation:

1) multiply 1,20,000×7

= 8,40,000

2) add 30,000 +90000

= 1,20,000

then divide 4,20,000÷1,20,000

= 3.5years = 3years 6months

Given,

Initial amount = Rs.90000

The amount given after every year = Rs. 30000

To Find,

The balance in the seventh year =?

In what year was the goal of Rs 420,000 met =?

Solution,

This is an AP as the common difference between each year is the same.

Therefore, a = Rs.90000 and d = Rs.30000

From the formula of the nth term in AP,

[tex]a_n = a +(n-1)d[/tex]

For the 7th year,

[tex]a_7 = 90000 +(7-1)30000\\a_7 = 90000 + 6*30000\\a_7 = 90000 + 180000\\a_7 = 270000[/tex]

For some value of n, the nth term is 420000

[tex]420000 = 90000 + (n-1)30000\\420000 - 90000 = (n-1)30000\\(n-1)*30000 = 330000\\n-1 = 330000/30000\\n-1 = 33/3\\n = 11 + 1\\n = 12[/tex]

Hence, the balance in the seventh year will be Rs. 270000 and after 12 years, the goal of Rs. 420000 was met.