A's 1 day's work = 1/15
B's 1 day's work = 1/20
C's 1 day's work = 1/25
A, B and C worked together.
? (A + B + C)'s 1 day's work = (1/15) + (1/20) + (1/25)
= (20 + 15 + 12)/ 300
= 47/300
Days taken to complete work by A, B and C working together = 300/47
? Share of C = (1/25) x (300/47) x 47000
= ? 1200
Ramesh's 1 day's work = 1/12
Suresh's 1 day's work = 1/16
(Ramesh + Suresh)'s 1 day work = (1/12) + (1/16)
= (16 + 12) / (12 x 16)
= 28/192
= 7/48
Given that, (Ramesh + Suresh + Boy)'s
1 day's work = 1/6
? Boy's 1 day's work = (1/6) - (7/48) = (8 - 7)/ 48 = 1/48
? Ramesh's share : Suresh's share : Boy's share = 1/12 : 1/16 : 1/48
= (8/96) : (6/96) : (2/96)
= 8 : 6 : 2
= 4 : 3 : 1
Let Ramesh's share be 4k , Suresh's share be 3k and boy's share be k.
According to the question,
4k + 3k + k = 800
8k = 800
? k = 800/8 = 100
? Ramesh's share = 4k = 4 x 100 = ? 400
Suresh's share = 3k = 3 x 100 = ? 300
Boy's share = k = ? 100
Let the number of days to complete the work be N.
According to the question,
k/20 + (k - 2)/24 + (k - 5)/ 30 = 1
? [6k + 5(k - 2) + 4(k - 5)] / 120 = 1
? 6k + 5k + 4k = 120 + 10 + 20
? 15k = 150
? k = 10
? Work done by A = 10/20 = 1/2
? Share of A from the assured money
= (1/2) x 5400
= ? 2700
Amount received by ( A + B + C) per day
= 5400/36 = ? 150
? A + B + C = ? 150.................(i)
Similarly, amount received by (A + C) per day
= 1880/20 = ? 94
? A + C = ? 94 ........................(ii)
Amount received by (B + C) per day
= 3040/40 = ? 76
? B + C = ? 76 ........................(iii)
From Eqs. (i) and (iii), we get
A + 76 = ? 150
A = 150 - 76 = ? 74
By putting the value of A in Eq. (ii), we get
74 + C = ? 94
? C = 94 - 74 = ? 20
Hence, amount received by C per day
= ? 20
Let the wages of 1 man, 1 woman and 1 boy are ? P, ? Q and ? R, respectively. According to the question,
3P + 2Q + 4R = 26 ....(i)
3P = 4Q ....(ii)
and 2Q = 3R ....(iii)
From Eqs. (i) and (ii), we get
4Q + 2Q + 4R = 26
? 6Q + 4R = 26.........................(iv)
From Eqs. (iii) and (iv), we get
9R + 4R = 26
? 13R = 26
? R = 2
From Eqs. (ii) and (iii), we get
Q = 3 and P = 4
? Wages of 4 men, 3 women and 2 boys
= (4 x 4) + (3 x 3) + (2 x 2)
= 16 + 9 + 4 = ? 29
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