Question

Four times the algebraic mean of \[x\] and \[10\], is \[70\], then what is the value of \[x\] ?
A) \[65\]
B) \[25\]
C) \[50\]
D) \[35\]

Answer 1

Hint: We solve this question by first applying the formula of algebraic mean, that is, sum of addends divided by number of addends, \[M = \dfrac{{{a_1} + {a_2} + {a_3}}}{3}\] , where \[{a_1},{a_2},{a_3}\] are addends, and M is their algebraic mean. Here we have four times the algebraic mean is \[70\] , so we first find the mean. Then we solve the linear equation for finding the value of \[x\]

Complete step by step solution:
We have formula of algebraic mean as sum of addends divided by number of addends, that is, , \[M = \dfrac{{{a_1} + {a_2}}}{2}\] , where \[{a_1},{a_2}\] are addends. Here in the question we have, 2 numbers that is \[x\] and \[10\] , on comparing with the general formula we get, \[{a_1} = x\] and \[{a_2} = 10\] , so the sum of addends will be \[x + 10\] and number of addends is \[2\]
So the algebraic mean of these two numbers will be
\[M = \dfrac{{x + 10}}{2}\]
Now, we are given that four times the algebraic mean of \[x\] and \[10\], is \[70\] , that is,
\[4M = 70\]
Substituting value of M, we get,
\[4\left( {\dfrac{{x + 10}}{2}} \right) = 70\]
Which becomes,
\[2\left( {x + 10} \right) = 70\]
Dividing both sides by 2, we get,
\[x + 10 = 35\]
Now, solving the linear equation for finding the value of x, we subtract 10 from both sides, we get,
\[x = 25\]
So, the correct answer is “Option B”.

Note: This question deals with the basic formula of algebraic mean that it is equal to quotient of sum of addends and number of addends, that can be written numerically as , \[M = \dfrac{{{a_1} + {a_2} + {a_3}}}{3}\] , where \[{a_1},{a_2},{a_3}\] are addends and M is their algebraic mean. Take care while doing the calculations.