Question

70% of a number is equal to 30% of another no .The average of both the no is 24, then find the larger number?

Answer 1

$\textbf{ Let the numbers are x( larger number ) and y( smaller number ),}$



$\underline{\text{According to the question :}}$

70 % of smaller number = 30% of larger number

70% of y = 30% of x

$\dfrac{70}{100} \times y = \dfrac{30}{100} \times x \\ \\ \\ \frac{7}{10} \times y = \frac{3}{10} \times x \\ \\ \\ 7y = 3x \\ \\ \frac{7y}{3} = x$




Then,
value of x in terms of x is 7y / 3



Given that the Average of both numbers is 24, so average of x and y is 24.


$\bold{ \mathsf{ \dfrac{sum \: of \: x \: and \: y \: }{ \: number \: of \: terms(x \: and \: y)} \: = average}}$


$\mathsf{ \dfrac{x + y}{2} = 24} \\ \\ \\ \frac{ \dfrac{7y}{3} + y}{2} = 24 \\ \\ \\ \frac{7y}{3} + y = 24 \times 2 \\ \\ \\ \frac{7y + 3y}{3} = 24 \times 2 \\ \\ \\ \frac{10y}{3} = 24 \times 2 \\ \\ \\ y = \frac{24 \times 2 \times 3}{10} \\ \\ y = 14.4$


Therefore other number is ( 7 × 14.4 ) / 3


Other number or x is 33.6




$\boxed{\bold{ \underline{ \mathfrak{ \mathsf{largr \: number = x = 33.6 }}}}}$