Question

If rupees 300 is divided into two parts such that 1/2 of the first part and 1/3 of the second part are equal, then find the difference of the two parts.​

Please help if you know the right answer ​

Answer 1

Let the two parts be, first part x and second part y

If rs 300 is divided in two parts

x + y = 300

x = 300 - y…Eq.1

1/2 of the first and 1/3 of the second are equal

1/2 × x = 1/3 × y

x/2 = y/3

3x = 2y…Eq..2

Now substituting the value of x from Eq.1 to Eq..2

3x = 2y

3 (300 - y) = 2y

900 - 3y = 2y

2y + 3y = 900

5y = 900

y = 900/5

y = 180

Thus second part is 180

Substituting value of y in Eq.1 to get the value of x

x = 300 -y

x = 300 - 180

x = 120

The first part is 120

Thus two parts are 120 and 180. Their difference

= 180 - 120 = 60

Answer the two parts are120 and 180 and their difference is 60

Now checking the correctness of answer by putting the value of x and y in Eq. 2

3x = 2y

3 × 120 = 2 × 180

360 = 360

Means answer is correct.