If 24 is subtracted from a number, the number gets reduced to its four-seventh. What is the sum of the digits of that number?

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Solution

The correct option is D 11
Let us assume the number as ‘n’.

According to the question,

If 24 is subtracted, it becomes $\frac{4}{7}$ of the number.

$n - 24 = n \times \frac{4}{7}$

$\Rightarrow n - \frac{4 n}{7} = 24$

$\Rightarrow \frac{(7 n - 4 n)}{7} = 24$

$\Rightarrow \frac{3 n}{7} = 24$

$\Rightarrow 3 n = 24 \times 7$

$\Rightarrow n = 24 \times \frac{7}{3}$

$\Rightarrow n = 8 \times 7$

$\Rightarrow n = 56$

Sum of the digits of the number $= 5 + 6 = 11$

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If 24 is subtracted from a number, the number gets reduced to its four-seventh. What is the sum of the digits of that number?

The correct option is D 11Let us assume the number as ‘n’. According to the question, If 24 is subtracted, it becomes 47 of the number. n−24=n×47 ⇒n−4n7=24 ⇒(7n−4n)7=24 ⇒3n7=24 ⇒3n=24×7 ⇒n=24×73 ⇒n=8×7 ⇒n=56 Sum of the digits of the number =5+6=11