Question

If 184 is divided into two parts such that one-third of one part exceeds one-seventh of the other part by 8, then the greater part is ?

Explain properly !

Answer 1

Let One Part Be = X

Then the other part will be = 184-X

One Third Of X = X/3

One seventh of another part = 184-X/ 7

Given :- one-third of one part exceeds one-seventh of other by 8 .

X/3 = 184-X /7+ 8

X/3 = 184-X + 56/7

7 x= 3( 240-x)

10x= 720

X= 72

Hence the two parts 72 and 112.

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Answer 2

Let the two parts is 'x' and 'y'.

(i)

Given that 184 is divided into two parts.

⇒ x + y = 184.  

⇒ x = 184 - y  ------ (1)

(ii)

Given that one-third of one part exceeds one-seventh of other part by 8.

⇒ (1/3)x = (1/7) y + 8

LCM of 3,7 = 21.

⇒ 7x = 3y + 168

⇒ 7(184 - y) = 3y + 168

⇒ 1288 - 7y = 3y + 168

⇒ 1288 - 168 = 10y

⇒ 1120 = 10y

⇒ y = 112.

Substitute y = 112 in (1), we get

⇒ x = 184 - y

⇒ x = 184 - 112

⇒ x = 72.

Therefore:

⇒ The two parts are 72 and 112.

⇒ The greater part is 112.

Hope it helps!