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# $x is enough for Bob to survive 45 days, while for Amy$x is enough to

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Math Expert
Joined: 02 Sep 2009
Posts: 64073
$x is enough for Bob to survive 45 days, while for Amy$x is enough to  [#permalink]

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27 Mar 2020, 03:53
00:00

Difficulty:

25% (medium)

Question Stats:

79% (02:00) correct 21% (01:46) wrong based on 71 sessions

$x is enough for Bob to survive 45 days, while for Amy$x is enough to survive only for 36 days. How many days they can survive together for total of $2x ? A. 10 days B. 20 days C. 30 days D. 40 days E. 50 days _________________ GMATWhiz Representative Joined: 07 May 2019 Posts: 693 Location: India Re:$x is enough for Bob to survive 45 days, while for Amy $x is enough to [#permalink] ### Show Tags 27 Mar 2020, 05:32 Bunuel wrote:$x is enough for Bob to survive 45 days, while for Amy $x is enough to survive only for 36 days. How many days they can survive together for total of$2x ?

A. 10 days
B. 20 days
C. 30 days
D. 40 days
E. 50 days

Solution

We can also solve it as time and work problem
• Let’s assume x as the LCM(45, 36)
o x = 180 units
• The amount required by Bob to survive one day = $$\frac{180}{45} = 4$$ units
• The amount required by Amy to survive one day = $$\frac{180}{36} = 5$$ units
o The amount required by both of them together to survive one day = $$4 + 5 = 9$$ units
o In 180 units they can survive = $$\frac{180}{9} = 20$$days
o With $$$x$$ they can survive = $$20$$ days o With$$$2x$$ they can survive =$$2*20=40$$ days
Hence, the correct answer is Option D.

Alternative method:

• The amount required by Bob to survive 45 days = x
o The amount required by Bob to survive 1 day = $$\frac{x}{45}$$
• The amount required by Amy to survive 36 days = x
o The amount required by Amy to survive 1 day = $$\frac{x}{36}$$
• Amount required by both of them to survive 1 day = $$\frac{x}{45} + \frac{x}{ 36} = \frac{(5x + 4x)}{180} = \frac{x}{20}$$
o With $$\frac{x}{20}$$ they both can survive 1 day
o With $$x$$, they can survive for 20days

If Bob can survive 45 days with $180, it means he uses up$4 per day. Similarly, Amy uses up $5 per day. These values represent the individual rates of Bob and Amy. If they have to survive together, they will consume a total of$9 per day. If a total of $360 is available, they can survive for a total of 40 days ($$\frac{360}{9}$$). The correct answer option is D. Hope that helps! _________________ Re:$x is enough for Bob to survive 45 days, while for Amy $x is enough to [#permalink] 31 Mar 2020, 23:19 #$x is enough for Bob to survive 45 days, while for Amy \$x is enough to

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