Question

The ratio of 2 numbers is \[\dfrac{5}{6}:\dfrac{2}{3}\], by what percentage is the second number more /less than the first number?
1. 20% less
2. 25% more
3. 25% less
4. 20% more

Answer 1

Hint: In this question, we need to find by what percentage is the second number more/less than the first number. The ratio of two numbers is given to us. So, firstly we will divide the difference of second number and first number and divide it by first number and then multiply it with 100.

Complete step-by-step solution:
We are given the percentage of the numbers. So, we will assume them as $\dfrac{5}{6}x$and $\dfrac{2}{3}x$.
Now, we will find the difference between the first number and second number by subtracting the second number from the first number. If the difference comes in negative numbers then the second number will be less than the first number and if the difference comes in positive numbers then the second number will be more than the first number.
$ = \dfrac{2}{3}x - \dfrac{5}{6}x$
Taking L.C.M. of the denominator,
$ = \dfrac{{4x - 5x}}{6}$
$ = \dfrac{{ - 1x}}{6}$
So, the second number is less than the first number.
Now we will find the percentage using its formula.
$ = \dfrac{{\dfrac{{ - 1x}}{6}}}{{\dfrac{{5x}}{6}}} \times 100$
$ = \dfrac{{ - 1}}{5} \times 100$
$ = - 20$
The second number is 20% less than the first number.
So, option (1) is the correct answer.

Note: A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”.
The least common multiple (L.C.M.) of two numbers is the ‘smallest non-zero common number’ which is a multiple of both the numbers.