Question : The average of the three numbers is 135. The largest number is 195 and the difference between the other two is 20. The smallest number is:
Option 1: 65
Option 2: 95
Option 3: 105
Option 4: 115
Correct Answer: 95
Solution :
Given:
The average of 3 numbers is 135.
The largest number is 195.
The difference between the other two is 20.
Let x be the smallest number.
So, (x + 20) would be the second number.
According to the question,
195 + x + x + 20 = 135 × 3
⇒ 2x + 215 = 405
⇒ 2x = 405 – 215 = 190
∴ x = $\frac{190}{2}$ = 95
So, the smallest number is 95.
Hence, the correct answer is 95.
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