Question

If one –third of a two digit number exceeds its one-fourth by 8, then what is the sum of the digits of the number?
a) 6
b) 13
c) 15
d) 17

Answer 1

Hint: Here we are dealing with fractions and we must know what fractions are. Fraction represents a part of a whole number or any number, in any number of equal parts. Assume the two digit number to be a variable x and then apply the given conditions and obtain the equation.

Complete step-by-step solution -
Explanation:
Step 1: Let the two digit number be x,
One-third of x will be, \[~\dfrac{1}{3}\times x~=\dfrac{x}{3}\]
One-fourth of x will be, $\dfrac{1}{4}\times x=\dfrac{x}{4}$
Now as given in question, c
 \[\dfrac{x}{3}-\dfrac{x}{4}~=\text{ }8\] this implies,
 \[~\dfrac{x}{12}=\text{ }8\] we get, \[x=96\]
Step 2: We get the two digit number\[96\] as and the sum of digits will be \[9+6\text{ }=\text{ }15\]. Hence, option c is correct.

Note: In this question we should let the number as a whole not be in form one and tenth digits. Means we can let numbers in terms of place value like $10x+y$ where x is tenth digit and y is unit digit. Then we can write the equation according to it. In this case we need a value of $x+y$ because we need to find the sum of digits.