Question

32. If rs. 782 be divided into three parts, proportional to 1/2 : 2/3 : 3/4 , then the first part is

Answer 1

Answer:

Rs 204

Step-by-step explanation:

Lcm of 2,3,4 =12

6x+8x+9x=782

x=34 Rs

First part 6x=6*34=Rs 204

Answer 2

Given - Amount

Find - First part

Solution - Let the three divided parts be 1/2x, 2/3x and 3/4x.

Representing the given information in equation form -

$\frac{x}{2} + \frac{2x}{3} + \frac{3x}{4} = 782$

Taking LCM, we get 12. Solving the fractions for value of x.

$\frac{x \times 6 + 2x \times 4 + 3x \times 3}{12} = 782$

$\frac{6x + 8x + 9x}{12} = 782$

Performing addition on Left Hand Side and shifting 12 to Right Hand Side

$23x = 12 \times 782$

Performing multiplication on Right Hand Side

$23x = 9384$

Performing division

$x = \frac{9384}{23}$

$x = 408$

Finding first part -

First part =

$\frac{1}{2} \times x$

First part =

$\frac{1}{2} \times 408$

First part =

$204$

Hence, the first part is 204.

Answer 3

Given - Amount

Find - First part

Solution - Let the three divided parts be 1/2x, 2/3x and 3/4x.

Representing the given information in equation form -

$\frac{x}{2} + \frac{2x}{3} + \frac{3x}{4} = 782$

Taking LCM, we get 12. Solving the fractions for value of x.

$\frac{x \times 6 + 2x \times 4 + 3x \times 3}{12} = 782$

$\frac{6x + 8x + 9x}{12} = 782$

Performing addition on Left Hand Side and shifting 12 to Right Hand Side

$23x = 12 \times 782$

Performing multiplication on Right Hand Side

$23x = 9384$

Performing division

$x = \frac{9384}{23}$

$x = 408$

Finding first part -

First part = $\frac{1}{2} \times x$

First part = $\frac{1}{2} \times 408$

First part = $204$

Hence, the first part is 204.