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At a bakery, Tom normally earns x dollars per hour of the first n hour

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At a bakery, Tom normally earns x dollars per hour of the first n hour [#permalink]

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New post 22 Jan 2018, 22:24
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58% (02:46) correct 42% (03:23) wrong based on 36 sessions

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At a bakery, Tom normally earns x dollars per hour of the first n hours of the day. For each hour he works in excess of n hours on a given day, he is paid 1.375 times his regular rate. If Tom decides to start working over time, what is the ratio of over time hours to regular time hours required to double his daily income?

A. 7 : 10
B. 375 : 100
C. 100 : 375
D. 11 : 8
E. 8 : 11
[Reveal] Spoiler: OA

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Re: At a bakery, Tom normally earns x dollars per hour of the first n hour [#permalink]

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New post 22 Jan 2018, 23:15
E

This question can easily be solved by assuming values.

Lets say tom earns 10$ per hour working for 8 hours normal time. his total earning is 80$.

Now wage for OT hours = 13.75$ per hour. this is to be equal to 80$ to make his income double.

Hence number of OT hours need to be worked is 80/13.75=35/6.

Hence ratio of OT hours to normal hours = 35/6/(8) = 8:11. option E
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At a bakery, Tom normally earns x dollars per hour of the first n hour [#permalink]

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New post 22 Jan 2018, 23:25
Bunuel wrote:
At a bakery, Tom normally earns x dollars per hour of the first n hours of the day. For each hour he works in excess of n hours on a given day, he is paid 1.375 times his regular rate. If Tom decides to start working over time, what is the ratio of over time hours to regular time hours required to double his daily income?

A. 7 : 10
B. 375 : 100
C. 100 : 375
D. 11 : 8
E. 8 : 11


Let a be the number of extra hours, so as per the question \(nx + a(1.375x) = 2nx\)
\(n = 1.375a\) or \(a/n = 8/11\)
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Re: At a bakery, Tom normally earns x dollars per hour of the first n hour [#permalink]

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New post 18 Feb 2018, 06:04
Let \(t\) be the total hours that Tom worked in a day, of which \(n\) are regular hours and \(t-n\) are overtime hours. We are asked to find the ratio of \(\frac{(t-n)}{n}\) such that Tom's income is double.

So for Tom to earn the double of his regular rate, the number of hours that he has to work can be expressed as -
\(nx+1.375(t-n)x = 2nx\)
\(n+1.375(t-n) = 2n\)
\(1.375(t-n) = n\)
\(\frac{(t-n)}{n}=\frac{1}{1.375}=\frac{8}{11}\)


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Re: At a bakery, Tom normally earns x dollars per hour of the first n hour   [#permalink] 18 Feb 2018, 06:04
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