A man and a boy received ? 800 as wages for 5 days for the work they did together. The man's efficiency in the work was three times that of the boy. What are the daily wages of the boy?

A, B and C contract to do a work for ? 4200. A can do the work in 6 days, B in 10 days and C in 12 days.
From given question, As we know that
A can do the work in 6 days.
A can do 1/6 work in one day.
B can do the same work in 10 days.
B can do 1/10 work in one day.
C can do the same work in 12 days.
C can do 1/12 work in one day.
Work done shared by A : B : C = 1/6 : 1/10 : 1/12
Multiply by 60, we will get,
Work done shared by A : B : C = 10 : 6 : 5
Let us assume ration variable is P.
According to question,
10P + 6P + 5P = 4200
? 21P = 4200
? P = 200
A's share = 10P = 10 x 200 = ? 2000
B's share = 6P = 6 x 200 = ? 1200,
C's share = 5P = 5 x 200 = ? 1000

A can do a work in 12 days.
? Work done by A = 1/12
B can do a work in 16 days.
? Work done by A = 1/16
Ration of Work done by A : Ration of Work done by B = 1/12 : 1/16
Ration of Work done by A : Ration of Work done by B = 4 : 3
A's shares = 2100 x 4/7 = 300 x 4 = ? 1200
B's share = 2100 x 3/7 = 300 x 3 = ? 900

The ratio of efficiency of man to boy
= 6 : 1
Efficiency ? Wages
? Boy's share = [1 / (1+6)] x 1400
(1/7) x 1400 = ? 200
Now, they worked for 10 days.
? Daily wages of a boy = 200/10 = ? 20

A's 1 day's work = 1/3
B's 1 day's work = 1/4
A's share : B's share
= (1/3) : (1/4) = (4/12) : (3/12)
= 4 : 3
A's share = (4/7) x 2800
= 4 x 400
= ? 1600

Let 1st person be X and 2nd person be Y.
Then, X's 1 day's work = 1/26
Y's 1 day's work = 1/39
X's share : Y's share
= 1/26 : 1/39 = 3/78 : 2/78 = 3 : 2
Difference of ratio = 3 - 2 = 1
? Required percentage = (1/2) x 100% = 50%
? 1 st person's wages is 50 % more than the 2nd person's wages.