Question

The sum of two numbers is 150. If one-fourth of the one exceeds one-sixth of the other by 5. The smaller number is

Answer 1

Step-by-step explanation:

first let the number and you will easily find the answers

Answer 2

The smaller number is 72.

Given,

The sum of two numbers is 150. One-fourth of the one exceeds one-sixth of the other by 5.

To Find,

The smaller number =?

Solution,

We can solve the question as follows:

It is given that the sum of two numbers is 150. One-fourth of the one exceeds one-sixth of the other by 5. We have to find the smaller number.

Let one of the numbers x and the other number be y.

$Bigger\: number = x\\Smaller\: number = y$

$x + y = 150$       -------- (1)

According to the question, 1/4 of x exceeds 1/6 of y by 5. Therefore,

$\frac{1}{4} x = \frac{1}{6} y + 5$

$\frac{x}{4} = \frac{y + 30}{6}$

$6x = 4(y + 30)$

$6x = 4y + 120$

Dividing all the terms by 2,

$3x = 2y + 60$

$3x - 2y = 60$      --------- (2)

Now, we will solve equations (1) and (2) to find the values of x and y.

From equation (1),

$x = 150 - y$

Substituting x = 150 - y in equation (2),

$3(150 - y) - 2y = 60$

$450 - 3y - 2y = 60$

$450 - 5y = 60$

$450 - 60 = 5y$

$5y = 390$

$y = \frac{390}{5} = 78$

Now, the value of x will be:

$x = 150 - 78 = 72$

Hence, the smaller number is 72.