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# Linda and Angela contract to paint a neighbor's house. Even though Lin

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Senior Manager
Joined: 29 Jan 2011
Posts: 334
Linda and Angela contract to paint a neighbor's house. Even though Lin [#permalink]

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23 Sep 2011, 01:16
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Difficulty:

85% (hard)

Question Stats:

42% (02:13) correct 58% (01:37) wrong based on 38 sessions

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Linda and Angela contract to paint a neighbor's house. Even though Linda spends 50% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?

A) 1/2 m
B) 1/3 m
C) 1/4 m
D) 1/5 m
E) 1/6 m

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/linda-and-an ... 26945.html
[Reveal] Spoiler: OA
Senior Manager
Joined: 29 Jan 2011
Posts: 334
Re: Linda and Angela contract to paint a neighbor's house. Even though Lin [#permalink]

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23 Sep 2011, 01:31
siddhans wrote:
Couldnt find after searching hence posting ...

Linda and Angela contract to paint a neighbor's house. Even though Linda
spends 50% more time painting the house than Angela, each receives a payment
of m dollars when the work is completed. If Angela decides to pay Linda n
dollars so that they would have received the same compensation per hour
worked, what is n in terms of m?

A)(1/2)m

B)(1/3)m

C)(1/4)m

D)(1/5)m

E)(1/6)m

I am stuck solving this in between

Let Angela worked x hours and
Let Linda worked 1.5 x hours

Total compensation both received = m$Thus hourly rate for Linda = (TOtal money received /No of hours worked) = m/1.5x Hourly rate for Angela = m/x Now Angela gives n dollars to Linda Thus Angela has m-n$

L's rate= m/(1.5)t $/h new rate for A=m-n/t L=(m+n)1.5t According to given conditions, the new rate for A & L must be equal (m-n)/t=(m+n)/(1.5t) or 3(m-n)=2(m+n) 3m -3n=2m+2n m=5n m=n/5 D _________________ Hit kudos if my post helps you. You may send me a PM if you have any doubts about my solution or GMAT problems in general. Senior Manager Joined: 29 Jan 2011 Posts: 334 Re: Linda and Angela contract to paint a neighbor's house. Even though Lin [#permalink] ### Show Tags 23 Sep 2011, 01:40 blink005 wrote: siddhans wrote: siddhans wrote: Couldnt find after searching hence posting ... Linda and Angela contract to paint a neighbor's house. Even though Linda spends 50% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m? A)(1/2)m B)(1/3)m C)(1/4)m D)(1/5)m E)(1/6)m I am stuck solving this in between Let Angela worked x hours and Let Linda worked 1.5 x hours Total compensation both received = m$

Thus hourly rate for Linda = (TOtal money received /No of hours worked) = m/1.5x

Hourly rate for Angela = m/x

Now Angela gives n dollars to Linda

Thus Angela has m-n $And Linda has m + n$

Now (m + n)/(1.5x) = (m-n)/x

Is this correct?

Yes

If i solve this further i get

m + n = 1.5 m + 1.5 n

Thus, 0.5m = 2 n

n= (5/20) m

n = (1/4) m

But OA is 1/5 m

What am i doing wrong here in calculations???
Manager
Joined: 20 Aug 2011
Posts: 139
Re: Linda and Angela contract to paint a neighbor's house. Even though Lin [#permalink]

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23 Sep 2011, 01:44
you wrote-
m + n = 1.5 m + 1.5 n

it's
m+n=1.5m-1.5n

0.5m=2.5n
m=5n
_________________

Hit kudos if my post helps you.
You may send me a PM if you have any doubts about my solution or GMAT problems in general.

Senior Manager
Joined: 29 Jan 2011
Posts: 334
Re: Linda and Angela contract to paint a neighbor's house. Even though Lin [#permalink]

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23 Sep 2011, 01:48
1
KUDOS
you wrote-
m + n = 1.5 m + 1.5 n

it's
m+n=1.5m-1.5n

0.5m=2.5n
m=5n

Thanks!!!
Manager
Joined: 14 Mar 2011
Posts: 196
Re: Linda and Angela contract to paint a neighbor's house. Even though Lin [#permalink]

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23 Sep 2011, 01:49
2
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1
This post was
BOOKMARKED
let angela work for 4hrs and get 600 rs. (m =600)

According to question, linda works 50% more time and gets the same amount. so let linda work 6hrs and get 600 rs.

so they do a total of 6 +4 =10 hrs of work and get 1200 rs together . The question basically asks to equalise their payment. so a total of 1200 rs is received by them and they do 10 hrs work together. average rate will be 1200/10 = 120 rs per hr. so linda should get 6.120 =720 rs. But she got only 600. so angela should give 120 rs to linda. answer = 120/600 =1/5

Manager
Joined: 20 Aug 2011
Posts: 139
Re: Linda and Angela contract to paint a neighbor's house. Even though Lin [#permalink]

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23 Sep 2011, 02:00
siddhans wrote:
you wrote-
m + n = 1.5 m + 1.5 n

it's
m+n=1.5m-1.5n

0.5m=2.5n
m=5n

Thanks!!!

That's okay, happens to most of us.

You're welcome.
_________________

Hit kudos if my post helps you.
You may send me a PM if you have any doubts about my solution or GMAT problems in general.

Director
Joined: 01 Feb 2011
Posts: 703
Re: Linda and Angela contract to paint a neighbor's house. Even though Lin [#permalink]

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25 Sep 2011, 12:59
L-------------A
150t/100------ t hours
$m-----------$m
$(m+n)--------$(m-n) after A gave away $n to L after A gave away$n to A ,their per hour charge became equal

=> (m+n) * ( 2/(3t)) = (m-n)/t

=> m = 5n => n = (1/5)*m

Current Student
Joined: 08 Jan 2009
Posts: 321
GMAT 1: 770 Q50 V46
Re: Linda and Angela contract to paint a neighbor's house. Even though Lin [#permalink]

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26 Sep 2011, 12:56
We are given two rates:
m / L
m / A

Following the payment of money, the following must hold:
(m+n) / L = (m-n) / A

We know that L = 1.5A, so its just a matter of getting rid of some variables and rearranging:

Lets cross multiply and rearrange:
A(m+n) = L(m-n)
m+n = L/A * (m-n)

Using L = 1.5A:
m+n = 1.5A/A * (m-n)
m+n = 1.5 * (m-n)

rearrange:
m+n = 1.5m - 1.5n
n+1.5n = 1.5m - m
2.5n = .5m
n = .5 / 2.5 * m
n = 1 / 5 * m

D)
Math Expert
Joined: 02 Sep 2009
Posts: 43378
Re: Linda and Angela contract to paint a neighbor's house. Even though Lin [#permalink]

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18 Dec 2017, 22:50
Linda and Angela contract to paint a neighbour's house. Even though Linda spends 50% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?

A) 1/2 m
B) 1/3 m
C) 1/4 m
D) 1/5 m
E) 1/6 m

After the final transaction:
Angela received $(m - n) for t hours; Linda received$(m + n) for 1.5t hours;

We are told that after that transaction they received the same compensation per hour $$\frac{(m - n)}{t}=\frac{(m+n)}{1.5t}$$:

$$1.5m-1.5n=m+n$$;

$$m=5n$$;

$$n=\frac{m}{5}$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/linda-and-an ... 26945.html
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Re: Linda and Angela contract to paint a neighbor's house. Even though Lin   [#permalink] 18 Dec 2017, 22:50
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