Question 27 of 51intermediate🔧 ApplyNumerical3 marks

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?

Correct Answer

10 years

Exercise: Exercise Set 8.2 | Q: 6 | (Page 13)
For More Understanding

Explanation

The problem involves an Arithmetic Progression where the first term is ₹5,00,000 and the common difference is ₹20,000. Using the nth term formula, we find n=11, meaning the 11th year salary is ₹7,00,000. Since the starting year is the 1st year, it takes 10 years of increments to reach the 11th year.

Solution Steps

  1. Step 1: Identify first term (a) = ₹5,00,000 and common difference (d) = ₹20,000.

  2. Step 2: Use the nth term formula: a_n = a + (n - 1)d

  3. Step 3: Substitute values: 7,00,000 = 5,00,000 + (n - 1) × 20,000

  4. Step 4: Simplify: 2,00,000 = (n - 1) × 20,000, so n - 1 = 10, giving n = 11.

  5. Step 5: Since n = 11 is the 11th year, the income reaches ₹7,00,000 after 10 years.

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