Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
The sum of four numbers is 64. If you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by 3, then all the results are equal. What is the difference between the largest and the smallest of the original numbers?
(a)21
(b)27
(c)32
(d)Cannot be determined
(e)None of these
Answer
Answer (as printed): C
Explanation
Let the four numbers be A, B, C and D. Let $A+3=B-3=3C=\frac{D}{3}=x$. Then, $A=x-3, B=x+3, C=\frac{x}{3}$ and $D=3x$. $A+B+C+D=64 \Rightarrow (x-3)+(x+3)+\frac{x}{3}+3x=64 \Rightarrow 5x+\frac{x}{3}=64 \Rightarrow 16x=192 \Rightarrow x=12$. Thus, the numbers are 9, 15, 4 and 36. Required difference $=(36-4)=32$.
Explanation as extracted from the printed page; notation may be imperfect.