The average of 13 numbers is 70. The average of the first five numbers is 60. The average of the next five numbers is 25% higher…

Question

The average of 13 numbers is 70. The average of the first five numbers is 60. The average of the next five numbers is 25% higher than the average of the first five numbers. The 11th number is 6 less than the 13th number, and the 12th number is 4 greater than the 13th number. What is the average of the 11th and 12th numbers?

1. A. 78 (Correct answer)
2. B. 77
3. C. 76
4. D. 74

Correct Answer

Option A — 78

Detailed Solution & Explanation

The correct answer is 78.

Key Points

• Convert every average to a total:
  • All 13 numbers: 13 × 70 = 910
  • First five: 5 × 60 = 300
  • Next five: their average is 25% above 60, i.e. 75, so the total is 5 × 75 = 375
• The first ten therefore account for 675, leaving 910 − 675 = 235 for the 11th, 12th and 13th.
• Let the 13th be x. Then the 11th is x − 6 and the 12th is x + 4:
  • (x − 6) + (x + 4) + x = 3x − 2 = 235 → x = 79
• So the 11th is 73 and the 12th is 83, and their average is (73 + 83)/2 = 78.

Additional Information

• Anchoring the unknowns to the 13th number is what keeps the algebra to a single variable — both other numbers are defined relative to it.
• "25% higher than 60" means 60 × 1.25 = 75, not 60 + 25.
• Check: 300 + 375 + 73 + 83 + 79 = 910 ✓, and 910 ÷ 13 = 70 ✓.

प्रश्न (हिन्दी में)

13 संख्याओं का औसत 70 है। पहली पाँच संख्याओं का औसत 60 है। अगली पाँच संख्याओं का औसत पहली पाँच संख्याओं के औसत से 25% अधिक है। 11वीं संख्या 13वीं संख्या से 6 कम है, और 12वीं संख्या 13वीं संख्या से 4 अधिक है। 11वीं और 12वीं संख्याओं का औसत क्या है?

1. A. 78
2. B. 77
3. C. 76
4. D. 74