Question 40 of 40intermediate🔧 ApplyNumerical4 marks

IQ of a person is given by the formula IQ=MACA×100\text{IQ} = \frac{\text{MA}}{\text{CA}} \times 100, where MA is mental age and CA is chronological age. If 80 ≤\leq IQ ≤\leq 140 for a group of 12 years old children, find the range of their mental age.

Correct Answer

The range of mental age is 9.6 ≤\leq MA ≤\leq 16.8 or MA lies between 9.6 years and 16.8 years (inclusive).

Exercise: Miscellaneous Exercise on Chapter 5 | Q: 14 | (Page Page 11)
For More Understanding

Explanation

This question tests the student's understanding of linear inequalities and their application. The student needs to substitute the given values into the IQ formula, form a compound inequality, and solve for MA by applying the rules of inequalities (multiplying/dividing by positive numbers preserves the inequality direction).

Solution Steps

  1. Step 1: Write the given inequality for IQ: 80 ≤\leq IQ ≤\leq 140

  2. Step 2: Substitute the formula for IQ: 80 ≤\leq (MA/CA) × 100 ≤\leq 140

  3. Step 3: Given CA = 12 years, substitute this value: 80 ≤\leq (MA/12) × 100 ≤\leq 140

  4. Step 4: Simplify: 80 ≤\leq (100 × MA)/12 ≤\leq 140

  5. Step 5: Multiply all parts by 12 (positive number, so inequality direction remains same): 80×1280 \times 12 ≤\leq 100 × MA ≤\leq 140×12140 \times 12 which gives 960 ≤\leq 100 × MA ≤\leq 1680

  6. Step 6: Divide all parts by 100: 960/100 ≤\leq MA ≤\leq 1680/100 which gives 9.6 ≤\leq MA ≤\leq 16.8

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