Question 23 of 44intermediate🔧 ApplyShort Answer3 marks

Subba Rao started work in 1995 at an annual salary of ₹ 5000 and received an increment of ₹ 200 each year. In which year did his income reach ₹ 7000?

Correct Answer

Subba Rao's income reached ₹ 7000 in the year 2005.

Exercise: EXERCISE 5.2 | Q: 19 | (Page Page 15)
For More Understanding

Explanation

This problem involves finding the number of terms in an Arithmetic Progression. The salaries form an AP with first term ₹ 5000 and common difference ₹ 200. Using the nth term formula, we find that ₹ 7000 is the 11th term. Since Subba Rao started in 1995, the 11th year corresponds to 1995 + 10 = 2005.

Solution Steps

  1. Step 1: Identify the AP parameters - First term (a) = ₹ 5000, Common difference (d) = ₹ 200, Last term (aₙ) = ₹ 7000

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

  3. Step 3: Substitute values: 7000 = 5000 + (n - 1) × 200

  4. Step 4: Solve for n: 7000 - 5000 = (n - 1) × 200 → 2000 = (n - 1) × 200 → n - 1 = 10 → n = 11

  5. Step 5: Calculate the year: Since Subba Rao started in 1995 (1st year), the 11th year = 1995 + 10 = 2005

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