Please helps to solve 2 math problem sum.?

Question

1) 108 adults were on board a train.After 1/3 of the men and
3/4 of the women alighted fm the train,there were 47 adults
left in the train.Find the number of women who alighted fm
the train.

2) Eugene and shashi had some picture cards each. Eugene gave 30% of his picture cards to Shashi.Shashi then gave 50% of his picture cards to Eugene.As a result,the ratio of Eugene picture card to Shashi picture card became 11:4.
a) What was the ratio of Eugene picture cards to Shashi picture cards at first?
b) If Shashi had 248 picture cards at the end,how many picture cards did he have at first?

Answer 1

1) 45w
2) a)2:1
b)620

Answer 2

Q1)
let the no. of men on board be M.
let the no. of women on board be W.

M + W = 108 ----- (E1)

108 - (1/3)M - (3/4)W = 47
(1/3)M + (3/4)W = 108 - 47
(4/12)M + (9/12)W = 61
4M + 9W = 61 * 12
4M + 9W = 732 ----- (E2)

using both equations,
(E2) - 4 * (E1):
(4M + 9W) - (4M + 4W) = 732 -108 * 4
5W = 732 - 432
5W = 300
W = 60

so the no. of women who alighted is 3/4 * 60 = 45.

Q2a)
let the no. of picture cards Eugene has be X.
let the no. of picture cards Shashi has be Y.

[0.5(0.3X + Y) + 0.7X] : 0.5(0.3X + Y) = 11 : 4

so,
0.85X + Y = 11 units ----- (E1)
0.15X + Y = 4 units ----- (E2)

using both equations,
(E1) - (E2):
(0.85X + Y) - (0.15X + Y) = 11 - 4
0.7X = 7
X = 10 units ----- (E3)

substitute (E3) into (E2):
(0.15) * 10 + Y = 4
Y = 4 - 1.5
Y = 2.5 units

hence the original ratio is 10 : 2.5. Simplifying it, the answer is 4 : 1.

Q2b)
at the end, Shashi had 4 units of cards.
at the beginning, Shashi had 2.5 units of cards.

hence, the no. of cards Shashi had at the beginning is:
248 * (2.5/4) = 155


hope all that helps! =)

Answer 3

(1). m/3 + 3w/4 + 47 = 108.

m/3 +3w/4 = 61

4m + 9w = 12*61 (taking L.C.M)

w = (732 - 4m) / 9.

To know the exact no. of women we should either know the no. of men or some more data is required.

Answer 4

If someone else answers these questions for you, you still won't know how to do them. The only thing to do is buckle down and tough it out.

Answer 5

m+w=108
m-m/3+w-3w/4=47
w=?