Nina, Oscar, and Elena each work at a constant rate. Nina and Oscar

Question

Nina, Oscar, and Elena each work at a constant rate. Nina and Oscar can complete a piece of work in 10 hours. Oscar and Elena can complete the same work in 15 hours. Elena and Nina can complete the same work in 12 hours. How many hours will Elena take to complete the work working alone?

A. 30
B. 32
C. 36
D. 40
E. 48

A. 30
B. 32
C. 36
D. 40
E. 48

M47-06

Bunuel · Accepted Answer

GMAT Club Official Solution:

Let Nina, Oskar, Elena rates be n, o, e jobs per hour.

n + o = 1/10
o + e = 1/15
e + n = 1/12

Sum the last two equations:
(o + e) + (e + n) = 1/15 + 1/12
o + 2e + n = 3/20

Subtract (n + o) = 1/10 = 2/20
2e = 3/20 - 2/20 = 1/20
e = 1/40

Time for Elena alone = 40

Answer: D

GMATFE2025 · Answer

Lets take the rate of work of Nina, Oscar, Elena as N | O | E. Work Volume = Rate*Time taken

Work Volume = (N+O)*10 = (O+E)*15 = (E+N)*12 = W

We have to calculate the hours Elena takes to complete the job.

N+O = W/10 (1) , O+E = W/15 (2), E+N = W/12 (3).

Subtract (3) from (1) = N+O - E -N = W/10-W/12 ====== O-E = W/60 (4) 
Subtract (4) from (2) = O+E-(O-E) = 2E = W/15-W/60 = W/20 ======== E=W/40 or 40E=W. So E takes 40 days to complete the job by themselves. Answer D.

Ujjwalk31 · Answer

Let N, O, and E be Nina's, Oscar's, and Elena's rates (work per hour). Then N+O=  \frac{1}{10} ,
O+E=  \frac{1}{15} , and
E+N= \frac{ 1}{12} .

Adding all three equations gives 2( N + O + E ) =  \frac{1}{10}  +  \frac{1}{15}  +  \frac{ 1}{12}  =  \frac{15}{60 }  =  \frac{1}{4}  , so, N+O+E=  \frac{1}{8 }  .

Thus, Elena's rate is E=  \frac{1}{8 }  −(N+O) =  \frac{1}{8 }  −  \frac{1}{10}  =  \frac{1}{40}  , and her time alone is  \frac{1}{40}  = 40 hours.

ANS = D

Dereno · Answer

The combined hours of

Nina + Oscar = 10 hours.

Oscar + Elena = 15 hours.

Elena + Nina = 12 hours.

Let the total work = LCM ( 10,15,12) = 60 units

So, the efficiency of :

Nina + Oscar = (60/10) = 6

Oscar + Elena = (60/15) = 4

Elena + Nina = (60/12) = 5

Adding the efficiency, we get

2*( Nina + Oscar + Elena) = 15

Nina + Oscar + Elena = (15/2)

we need to find : Elena

Elena = (15/2) - (Nina + Oscar)

= (15/2) - 6

= 3/2.

Number of days of Elena = 60/(3/2) = (60*2)/3 =  40

Option D

Vivek1707 · Answer

One quick way which involves fewer fractions to deal with:

Let total work be LCM of 10 , 15 , 12 i.e 60 units

N and O can do 6 units per hour
O and E can do 4 units per hour
E and N can do 5 units per hour

Add them up
2 (N + O + E) = 15 units per hour 
or
(N + O + E) = 7.5 units per hour
Replace N + O from above 
6+E = 7.5
So E = 1.5

Hence E will take 60/1.5 i.e 40 hours to complete the work

Nina, Oscar, and Elena each work at a constant rate. Nina and Oscar

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Nina, Oscar, and Elena each work at a constant rate. Nina and Oscar

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