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# The product of the cost per head and the number of people going for a

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Math Expert
Joined: 02 Sep 2009
Posts: 61302
The product of the cost per head and the number of people going for a  [#permalink]

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28 Dec 2019, 00:33
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Difficulty:

65% (hard)

Question Stats:

50% (02:03) correct 50% (02:33) wrong based on 12 sessions

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The product of the cost per head and the number of people going for a picnic is constant. When 10 more people join in the cost per head decreases from Rs. 40 to Rs. 36. What will be the decrease in cost per head if further 20 more people join in?

A. 2
B. 4
C. 6
D. 8
E. 12

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The product of the cost per head and the number of people going for a  [#permalink]

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21 Jan 2020, 04:03
Bunuel wrote:
The product of the cost per head and the number of people going for a picnic is constant. When 10 more people join in the cost per head decreases from Rs. 40 to Rs. 36. What will be the decrease in cost per head if further 20 more people join in?

A. 2
B. 4
C. 6
D. 8
E. 12

The question is barely in English ("if further 20 more people join in") and it makes it seem the number of people is a variable, when it's not. It also hardly makes sense for the product of the cost per person and the number of people to be constant, because then the picnic costs the same whether 2 people attend or 2,000,000. So it's not a good question (where is it from?).

The product the question says is constant, the cost per head times the number of people, is just the total cost of the picnic, so that's what I'll call it. The total cost is constant, so is the same for any number of people. If we have p people, and it costs \$40 per head, the total cost is 40p. We know that the cost per person goes down to \$36 when we add 10 people, so the total cost is also equal to 36(p + 10). Since the total cost is a constant, these must equal each other, so

40p = 36p + 360
p = 90

and we have 90 people originally. Since it costs \$40 per head, the total cost is 40*90= \$3600. If we add a further 20 to the 10 we added before, we'll have 120 people, and for the total cost to still be \$3600, it must now cost \$30 per head. Now it's not altogether clear what decrease the question is asking for (from the original 90 people or from the 100 people after ten are added) but from the answer choices, I gather it's the latter, so the answer is \$6, since the cost per head drops from \$36 to \$30.
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The product of the cost per head and the number of people going for a   [#permalink] 21 Jan 2020, 04:03
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