An amount of $351.78 is to be distributed as wages amongst a man, a wo

Question

An amount of $351.78 is to be distributed as wages amongst a man, a woman and a boy. The man worked for 27 days, the woman for 23 days and the boy for 19 days. The woman and the boy together can do the same amount of work that the man does and the man and the boy together can do 1.5 times the work that the woman does in a fixed time. How much would the man earn?

(A) $190.60
(B) $193.05
(C) $195.50
(D) $195.90
(E) $196.90

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Official Answer

B

(A) $190.60
(B) $193.05
(C) $195.50
(D) $195.90
(E) $196.90

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Regor60 · Answer

The challenge presented by this problem shouldn't include decimals multiplied by decimals.

This can be fixed by making the amount to be distributed a multiple of 82

Posted from my mobile device

Ayush2704 · Answer

According to question -
W+B = M ---------- (1)
M+B= 1.5W ---------- (2)
So, W+2B = 1.5W
Therefore, 2B=0.5W

So, (Wx0.5)/2 = B ------- (3)

Similarly, putting value of B in (1)
W + (Wx0.5)/2 = M
So, on solving the above equation we get,
2.5W/2 = M --------- (4)

Now efficiency of Man, Woman and Boy comes out to be -

(Wx2.5)/2 : W : (Wx0.5)/2 ------- (5)

On solving equation (5) we get 
Efficiency of Man: Woman: Boy - 5:4:1

Now Work done by Man, Woman and Boy is 27 days, 23 days and 19 days respectively, hence

Total Work done = (5x27) + (4x23) + (1x19) = 135 units + 92 units + 19 units 
=246 units

Hence, earning of man = (Work done by A/ Total work done) x Total amount
= (135/246) x 351.78 
= 193.05

Hence option B

Kinshook · Answer

Given: An amount of $351.78 is to be distributed as wages amongst a man, a woman and a boy. The man worked for 27 days, the woman for 23 days and the boy for 19 days. The woman and the boy together can do the same amount of work that the man does and the man and the boy together can do 1.5 times the work that the woman does in a fixed time.

Asked: How much would the man earn?

Let us assume that wages of a man, a woman and a boy be m, w & b respectively

m = w + b
m + b = 1.5w
w + 2b = 1.5w
.5w = 2b
w = 4b
m = w + b = 5b

27m + 23w + 19b = 351.78
27*5b + 23*4b + 19b = 351.78
135b + 92b + 19b = 351.78
246b = 351.78
b = 351.78/246

Earning of the man = 27m = 27*5b = 135*351.78/246 = $193.05

IMO B

VishvaT · Answer

While I got the answer, I got stuck at 135*351.78/246. How would you calculate that in a GMAT without calculator in the time frame?

An amount of $351.78 is to be distributed as wages amongst a man, a wo

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An amount of $351.78 is to be distributed as wages amongst a man, a wo

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