Harish started work at an annual salary of ₹ 5,00,000 and received an increment of ₹ 20,000 each year. Class 9

Harish started work at an annual salary of ₹ 5,00,000 and received an increment of ₹ 20,000 each year. Class 9

Question 1.

Harish started work at an annual salary of ₹ 5,00,000 and received an increment of ₹ 20,000 each year. After how many years did his income reach ₹ 7,00,000? Class 9

Solution:

Given,

a = 5,00,000, d = 20,000,

Suppose after n years his income reaches ₹ 7,00,000.

∴ t_n = 7,00,000

∴ a + (n - 1) d = 7,00,000

∴ 7,00,000 = 5,00,000 + (n - 1) × 20,000

∴ 2,00,000 = (n - 1) × 20,000

∴ n - 1 = 10

∴ n = 11

∴ Income reaches ₹ 7,00,000 after 11 years.

Question 2.

A child arranges marbles in rows so that the first row has 1 marble, the second has 2 marbles, the third has 3, and so on up to 25 rows. How many marbles does the child use in all? Class 9

Solution:

The number of marbles in each row forms a

sequence 1, 2, 3,..., 25

The sum of the first n natural numbers is.

S_n = $\frac{n(n+1)}{2}$

∴ S₂₅ = $\frac{25 \times 26}{2}$

∴ S₂₅ = 25 × 13

∴ S₂₅ = 325

∴ The child uses 325 marbles in all.