Question

divide 300 into parts such that the second part is half of the first part that the third part is 3 times of the second part. find the three different parts​

Answer 1

Answer:

100,50 & 150

Step-by-step explanation:

As per the provided information in the given question, we have :

• Total amount = 300
• The second part is half of the first part.
• The third part is 3 times of the second part.

We are asked to divide 300 into three parts as per the given conditions.

Let us assume the first part as x.

As per the conditions,

$\longmapsto \rm {First \; part = x }$

$\longmapsto \rm {Second \; part = \dfrac{x}{2}}$

• Since, the second part is half of the first part.

$\longmapsto \rm {Third \; part = \dfrac{3x}{2}}$

• Since, the third part is 3 times of the second part.

Now, as the total amount is divided in three parts so the sum of all these three parts will be equal to the total amount. Writing it in the form of equation,

$\longmapsto\rm {x + \dfrac{x}{2} + \dfrac{3x}{2} = 300 }$

Taking the L.C.M and making the denominator same in the L.H.S.

$\longmapsto\rm { \dfrac{2x + x + 3x}{2}= 300 }$

Performing addition in the numerator of the fraction in the L.H.S.

$\longmapsto\rm { \dfrac{6x}{2}= 300 }$

Transposing 2 from L.H.S to R.H.S. Its arithmetic operator will get changed in R.H.S.

$\longmapsto\rm { 6x= 300(2) }$

Multiplying 2 with 300 in L.H.S.

$\longmapsto\rm { 6x= 600 }$

Transposing 6 from L.H.S to R.H.S. Its arithmetic operator will get changed in R.H.S.

$\longmapsto\rm { x =\cancel{ \dfrac{600}{6}} }$

Dividing 600 by 6.

$\longmapsto\bf { x = 100 }$

Therefore,

$\longmapsto \rm {First \; part = x }$

$\longmapsto \bf {First \; part = 100 }$

Finding 2nd part,

$\longmapsto \rm {Second \; part = \dfrac{x}{2}}$

Substitute the values of x.

$\longmapsto \rm {Second \; part = \dfrac{100}{2}}$

$\longmapsto \bf {Second \; part = 50 }$

Finding 3rd part,

$\longmapsto \rm {Third \; part = \dfrac{3x}{2}}$

Substitute the values of x.

$\longmapsto \rm {Third \; part = \dfrac{3(100)}{2}}$

$\longmapsto \rm {Third \; part = \dfrac{300}{2}}$

$\longmapsto \bf {Third \; part = 150 }$

∴ The required parts are 100,50 & 150.