0 vote
Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 105 more than the smallest number, find the largest number.
Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 105 more than the smallest number, find the largest number.
1). 315
2). 378
3). 372
4). Cannot be determined
1 answers
3 vote
Let the first number be = 3x
Let the second number be = 6x
Let the third number be = 2x
Average of the three numbers is given to be 105 + 2x
$(Average\; = \;\frac{{Sum\;of\;all\;observations}}{{Number\;of\;observations}})$
$(\begin{array}{l} \Rightarrow 105 + 2x = \frac{{3x + 6x + 2x}}{3}\\ \Rightarrow 105 + 2x = \frac{{11x}}{3}\\ \Rightarrow 105 = \frac{{11x}}{3} - 2x\\ \Rightarrow 105 = \frac{{11x - 6x}}{3}\\ \Rightarrow 105 = \frac{{5x}}{3}\\ \Rightarrow x = \frac{{105\; \times \;3}}{5}\\ \Rightarrow x = 21 \times 3 \end{array})$
⇒ x = 63
⇒ 6x = 6 × 63 = 378