In two types of powdered detergent the ratio of soda and soap-dust is 2:5 and 3:4. If 10 kg of the first type is mixed with 15 kg of the second type, find the ratio of soda to soap-dust in the new detergent mixture.
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first types=2x ,5x
second types=3y,4y
2x+3y=10.................(1)
5x+4y=15.................(2)
equation (1) multiple by 5 and, equation (2) multiple by 2.
5(2x+3y=10) =10x+15y=50..........(3)
2(5x+4y=15) =10x+20y=30...........(4)
substitute (3) and (4) equation
-5y=20
[y=-4]
put the value y in equation (1)
2x+3(-4)=10
2x=10+12
x=22/2
[x=11]
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