The ratio of the number of stamps Weiming has to the number of stamps Rajuhas is 9 : 5. After Weiming gives Raju 8 stamps, the ratio becomes 4 : 3. Howmany stamps do Weiming and Raju have altogether?
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The ratio of the number of stamps Weiming has to the number of stamps Rajuhas is 9 : 5. After Weiming gives Raju 8 stamps, the ratio becomes 4 : 3. Howmany stamps do Weiming and Raju have altogether?
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Answer:
Number of stamps John had at first = 42
SOLUTION :
Let ‘x’ and ‘y’ be the initial stamps held by John and Mary respectively.
y/x = 3/7
=> 7y = 3x
=> 7y-3x =0 ……………..Eq.1
After 6 stamps received by Mary, the ratio is
(y+6)/(x-6) = 4/6
=> 6y+36 = 4x-24
=> 6y-4x = -60 ………….Eq.2
By Multiplying Eq.1 both sides with 4 , we get
28y-12x = 0 ……………..Eq.3
By Multiplying Eq.2 both sides with 3, we get
18y-12x= -180 ………….Eq.4
By subtracting Eq.4 from Eq.3, we get
10y = 180
=> y= 18
By substituting‘y’ value in Eq.1, we get
7(18)-3x = 0
=> 126–3x =0
=> 3x = 126
=> x = 42