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15 Jul 2026, 10:47
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work-rate word problem
M did 1/4 of work. F did next 50% so 1/4 to 3/4 hence 1/2 work and N did remaining 1/4 work.
Let time of F be x.
we are given N time is 2 hrs. total of F + N time is x+2
we are given M time is 1/2 of total time. so rest half is F+N
Let total time be t.
M time is t/2 & x+2 = t/2 hence t=2(x+2) .
M time = t/2 = (x+2)
so M rate is (1/4)/(x+2) = 1/4(x+2)
N rate is (1/4)/2 = 1/8
F rate is 1/(2x)
Q: what is M+F working together time?
M+F together working rate = 1/4(x+2) + 1/(2x) = (3x+4)/4x(x+2)
M+F together working time to complete whole work is reciprocal of this = 4x(x+2)/(3x+4)
if we find x we can answer the question. so essentially we are looking for x
i) x=4 sufficient
ii) (x+2) + 2 = 2x. we can solve for x hence sufficient.
D
M did 1/4 of work. F did next 50% so 1/4 to 3/4 hence 1/2 work and N did remaining 1/4 work.
Let time of F be x.
we are given N time is 2 hrs. total of F + N time is x+2
we are given M time is 1/2 of total time. so rest half is F+N
Let total time be t.
M time is t/2 & x+2 = t/2 hence t=2(x+2) .
M time = t/2 = (x+2)
so M rate is (1/4)/(x+2) = 1/4(x+2)
N rate is (1/4)/2 = 1/8
F rate is 1/(2x)
Q: what is M+F working together time?
M+F together working rate = 1/4(x+2) + 1/(2x) = (3x+4)/4x(x+2)
M+F together working time to complete whole work is reciprocal of this = 4x(x+2)/(3x+4)
if we find x we can answer the question. so essentially we are looking for x
i) x=4 sufficient
ii) (x+2) + 2 = 2x. we can solve for x hence sufficient.
D
15 Jul 2026, 10:54
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Lets assure rate % completed Time spent also assume total time spent as T hours
Maya- a 25 T/2
Felix b 50 (T/2)-2
Nora c 25 2 Hours
a=25/(T/2)=50/T
b= 50/((T/2)-2)= 100/(T-4)
c= 25/2= 12.5
Lets find out sufficiency of finding how many hours would it take Maya and Felix to work together at their constant rate from start to finish this Mural, on the basis of given two statements one by one
Statement-1: Felix took 4 hours
That means we know (T/2)-2= 4 that gives T=12
If we know T=12 we know a, b, c all rate and then we can easily find how much time would it take Maya and Felix together at their own constant rate working together from start to finish.
we don't need to actually find value in data sufficiency, we know all variables required to calculate and we can calculate, That's enough to say it is sufficient to answer
Statement-1 is sufficient
Statement-2: Time Maya and Nora spent= 2 time time Felix spent
T/2+2= 2*((T/2) - 2) that implies T/2 +2 = T - 4 T implies T/2=6 and T=12
Again it is similar to statement-1 we know total time T=12, we can find individual rate and calculate what is being asked for.
Statement-2 is also sufficient
Each statement alone is sufficient
Maya- a 25 T/2
Felix b 50 (T/2)-2
Nora c 25 2 Hours
a=25/(T/2)=50/T
b= 50/((T/2)-2)= 100/(T-4)
c= 25/2= 12.5
Lets find out sufficiency of finding how many hours would it take Maya and Felix to work together at their constant rate from start to finish this Mural, on the basis of given two statements one by one
Statement-1: Felix took 4 hours
That means we know (T/2)-2= 4 that gives T=12
If we know T=12 we know a, b, c all rate and then we can easily find how much time would it take Maya and Felix together at their own constant rate working together from start to finish.
we don't need to actually find value in data sufficiency, we know all variables required to calculate and we can calculate, That's enough to say it is sufficient to answer
Statement-1 is sufficient
Statement-2: Time Maya and Nora spent= 2 time time Felix spent
T/2+2= 2*((T/2) - 2) that implies T/2 +2 = T - 4 T implies T/2=6 and T=12
Again it is similar to statement-1 we know total time T=12, we can find individual rate and calculate what is being asked for.
Statement-2 is also sufficient
Each statement alone is sufficient
15 Jul 2026, 11:03
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IMO D
As per Q, let felix takes x hours
If maya & felix completed entire mural then their combine rates = 1/8x +1/4(2+x)
reversing & solving for x give the result
St 1: x=4 hrs, sufficient
St2: 2+x +2 = 2*(x), sufficient
Hence both st are suffiecient alone.
As per Q, let felix takes x hours
| Time | Work | |
| Nora | 2 | 5/8 |
| Felix | x | 1/8 |
| Maya | 2+x | 1/4 |
reversing & solving for x give the result
St 1: x=4 hrs, sufficient
St2: 2+x +2 = 2*(x), sufficient
Hence both st are suffiecient alone.
Bunuel
15 Jul 2026, 11:05
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Let rates be m,f,n
1/4n =2
n=1/8
1/4m = 0.5*(1/4m + 1/2f + 2)
1/4m - 1/2f =2....Eq.1
reqd = 1/m+f
m+f=??
1. 1/2f = 4
1/4m -4=2...from Eq.1
m can be find out...SUFFICIENT
2. 1/4m +2 =2* 1/2f
using Eq.1
1/f=4
1/4m + 2=4
m can be find out..SUFFICIENT
Ans D
1/4n =2
n=1/8
1/4m = 0.5*(1/4m + 1/2f + 2)
1/4m - 1/2f =2....Eq.1
reqd = 1/m+f
m+f=??
1. 1/2f = 4
1/4m -4=2...from Eq.1
m can be find out...SUFFICIENT
2. 1/4m +2 =2* 1/2f
using Eq.1
1/f=4
1/4m + 2=4
m can be find out..SUFFICIENT
Ans D
