3 men and 4 children together in 7 days earn 756rs. 11 men and 13 children together in 8 days earn 3008rs. in how many days will 7 men and 9 children together earn 2480Rs .
Answers
The answer is 10 days.
To find the answer we first simplify the given data by replacing the men with "X" and childs with "Y".
Thus from the first relation we know that
(3X + 4Y) × 7 = 756
=> 3X + 4Y = 108 ..........................eq(1)
And from the second relation we have
(11X + 13Y) × 8 = 3008
=> 11X + 13Y = 376 .......................eq(2)
Required is to find the number of days in which 7 men and 9 childs would earn 2480
=> (7X + 9Y) × days = 2480 ...........eq(3)
Now we have to find the values of X and Y from the above two equations .:
multiplying eq(1) by "11" and eq(2) by "3"
=> 33X + 44Y = 1188
& 33X + 39Y = 1128
________________________(subtract)
=> 0 + 5Y = 60
=> Y = 60/5
=> Y = 12
Now putying the value of Y in eq(1)
=> 3X + 48 = 108
=> X = (108-48)/3
=> X = 60/3
=> X = 20
Now putting the value of X and Y in equation 3 .:
(140 + 108) × days = 2480
=> days = 2480/248