Question

Divide 600 into 2 parts such that 40% of one exceeds 60% of the other by 120

Answer 1

Solution:-
Let the one part be 'x' and the other part be 600 - x
Therefore, according to the question.
(x × 40)/100 = {(600 - x) × 60}/100 + 120
On solving both L.H.S. and R.H.S. we get
2x/5 = {(600 - x)3}/5 + 120
2x/5 = (1800 - 3x)/5 + 120
Taking L.C.M of (1800 - 3x)/5 + 120/1, and solving it, we get
2x/5 = (1800 - 3x + 600)/5
2x + 3x = 1800 + 600
5x = 2400
x = 2400/5
x = 480
Therefore the first part is 480 and the other is 600 - 480 = 120
Answer.


Let us cross check the answer.
1st part = 480 and 2nd part = 120
40 % of the first part exceeds 60 % of the other by 120.
40 % of 480 = 60 % of 120 + 120
192 = 72 + 120
192 = 192
L.H.S. = R.H.S.
Hence proved.