Question

In two types of powder detergent the ratio of soda and soap dust is 2:19 and 1:11 respectively. If 7 kg of the first type is mixed with 4 kg of the second type,find the ratio of soda and soap dust in the new detergent mixture .
a) 20:1 b)1:10
C)9:1 d)1:9

Answer 1

The ratio of soda and soap dust in the new detergent mixture is option (b):- 1:10.

Step-by-step explanation:

The ratio of soda and soap dust in the first type of detergent = 2:19

The ratio of soda and soap dust in the second type of detergent = 1:11

It is given that the 7 kg of the 1st type is mixed with 4 kg of the 2nd type to get a new detergent mixture, therefore,

The quantity of soda in the new detergent mixture is

= $[\frac{2}{19+2}*7] + [\frac{1}{11+1} * 4]$

= $[\frac{2}{21} * 7] + [\frac{1}{12} * 4]$

= $\frac{2}{3} + \frac{1}{3}$

= $\frac{3}{3}$

= 1 ….. (i)

And,

The quantity of soap dust in the new detergent mixture is

= $[\frac{19}{19+2} * 7] + [\frac{11}{1+11} *4]$

= $[\frac{19}{21}*7] + [ \frac{11}{21} * 4]$

= $\frac{19}{3} + \frac{11}{3}$

= $\frac{30}{3}$

= 10 …… (ii)

Thus, from (i) & (ii), we get

The ratio of soda and soap dust in the new detergent mixture is  

= 1 : 10

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