On a cruise, 60% of the passengers were adults and 40% were

Question

On a cruise, 60% of the passengers were adults and 40% were children. The adults consisted of men and women. On the return cruise, the number of men decreased by 20%, the number of women decreased by 10%, and the number of children increased by 50%. The total number of passengers increased by 9.5%. On the first cruise, what percent of the adults were men?

A. 45%
B. 60%
C. 70%
D. 75%
E. 80%

A. 45%
B. 60%
C. 70%
D. 75%
E. 80%

Dereno · Answer

Let the total population be 100.

60%(100) = 60 are adults = men + women.

40%(100) = 40 are children.

100 = m + (60-m) + 40

The population increased by 9.5% = 109.5

The men decreased by 20% = 0.2 , and the value becomes 0.8m

The women decreased by 10% = 0.1, and the value becomes 0.1*(60-m)

The children population increased by 50% = 20

So, the value  9.5 = -0.2m - 0.1(60-m) +20

Solving, we get

9.5 = 14 - 0.1m

m = (4.5/0.1)

m = 45

Fraction of adults who are men = 45/60 = (3/4) =  75%

Option D

suntprovident · Answer

Is it usual for this question to take 21⁄2 to 3 mins or I need to practice to reduce this to under 2 mins

vasu1104 · Answer

total - 100x
adults = 60x
say men= p
women= 60x - p

children = 40x

return trip=
total= 109.5x
men = (4/5)p
women = (9/10) (60x-p)
children = 60x

(4/5)p + (9/10) (60x-p) + 60x = 109.5x

upon solving this , we get p = 45x

now we need to find the P / 60x
45x/60x
75%

egmat · Answer

Hi there,

Let's assume the first cruise had  100  total passengers.

- Adults =  60%  of  100  =  60 
- Children =  40%  of  100  =  40 
- Let Men = M, so Women =  60  - M

Now set up the return cruise using the given percentage changes:

- Men decreased by  20% :  0.8 M
- Women decreased by  10% :  0.9 ( 60  - M)
- Children increased by  50% :  1.5  ×  40  =  60

The total passengers increased by  9.5% , so the return cruise had  109.5  passengers.

Now write the equation:

0.8 M +  0.9 ( 60  - M) +  60  =  109.5

Expand:
 0.8 M +  54  -  0.9 M +  60  =  109.5

Combine like terms:
- 0.1 M +  114  =  109.5

- 0.1 M = - 4.5

M =  45

So there were  45  men out of  60  adults.

45  /  60  =  0.75  =  75%

Answer: D

The most common mistake here is calculating men as a percent of total passengers ( 45% ) instead of as a percent of adults ( 75% ).  The question specifically asks what percent of the adults were men, not what percent of all passengers.

Key principle:  Always re-read what the question asks for — the denominator matters!

On a cruise, 60% of the passengers were adults and 40% were

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On a cruise, 60% of the passengers were adults and 40% were

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