Question

A man saved ₹ 7,65,000 in 10 years. In each year, after the first, he saved ₹ 6,000 more than he did in the preceding year. How much did he save in the first seven years.

Answer 1

Total saving in 10 years = ₹ 7,65,000

Each year he saved ₹ 6,000 more than previous year

d = 6000

Let his first year saving be ₹ a.

Number of years (n) = 10

By formula,

\[S_n = \frac{n}{2}[2a + (n - 1)d]\]

Substituting values, we get:

⇒ \[765000 = \frac{10}{2}[2a + 9(6000)]\]

⇒ \[765000 = 5[2a + 54000]\]

⇒ \[765000 = 10a + 270000\]

⇒ \[10a = 765000 - 270000\]

⇒ \[10a = 495000\]

⇒ \[a = \frac{495000}{10}\]

⇒ \[a = 49500\]

Savings in the first seven years:

⇒ \[S_7 = \frac{7}{2}[2(49500) + (7 - 1)(6000)]\]

\[{} = 3.5[99000 + 6(6000)]\]

\[{} = 3.5(99000 + 36000)\]

\[{} = 3.5(135000)\]

\[{} = \text{₹}\,4{,}72{,}500.\]

Hence, amount saved in first 7 years = ₹ 4,72,500