Question

Two numbers are in the ratio 2 : 3 and if 5 is subtracted from each they are reduced to the ratio 3 : 5.

Find the smaller number.​

Answer 1

Step-by-step explanation:

Let the numbers be 2x,3x.

Then, 2x-5/3x-5=3/5

By cross multiplying with each other, we get

• (2x-5)*5=(3x-5)*3
• 10x-25=9x-15
• 10x-9x=-15+25
• x=10
• therefore, the smallest number is 2*x=2*10=20

Hope you understood...

Answer 2

Concept

An algebraic equation can be defined as a mathematical statement in which two expressions are equal to each other. An algebraic equation usually consists of a variable, coefficients, and constants.

Given

It is given that two numbers are in the ratio 2 : 3 and if 5 is subtracted from each they are reduced to the ratio 3 : 5.

Find

We need to find the smaller number

Solution

Let the two numbers be x and y.

According to the question, x/y = 2/3

x=2y/3

If 5 is subtracted from each they are reduced to the ratio 3 : 5.

x-5/y-5 =3/5

5(x-5) = 3(y-5)

5x-25 = 3y-15

5x-3y=10.....(1)

Put x =2y/3 in equation (1), we get

5(2y/3) -3y=10

10y/3 - 3y=10

10y-9y/3 =10

y/3=10

y=30

x=2y/3=2(30)/3=20

Hence the value of smallest number is x=20

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