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

Question

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

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Official Answer

D

siddhans · Answer

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

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

blink005 · Answer

A's rate =m/t $/h
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

siddhans · Answer

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???

blink005 · Answer

Sign error on your part-
you wrote-
m + n = 1.5 m + 1.5 n

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

0.5m=2.5n
m=5n

siddhans · Answer

<img src="{SMILIES_PATH}/icon_redface.gif" alt=":oops:" title="Embarassed" /> <img src="{SMILIES_PATH}/icon_redface.gif" alt=":oops:" title="Embarassed" /> <img src="{SMILIES_PATH}/icon_redface.gif" alt=":oops:" title="Embarassed" />

Thanks!!! <img src="{SMILIES_PATH}/icon_wink.gif" alt=":wink:" title="Wink" />

Aj85 · Answer

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

answer D

blink005 · Answer

That's okay, happens to most of us.

You're welcome.

Spidy001 · Answer

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

Answer is D.

pike · Answer

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)

Bunuel · Answer

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 $\frac{(m - n)}{t}=\frac{(m+n)}{1.5t}$:

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

$m=5n$;

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

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/linda-and-an ... 26945.html

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