Question 56

Two numbers are in the ratio of 7 : 5. On diminishing each of them by 40, the ratio becomes 27 : 17. The sum of the numbers is:

Solution

let two numbers be X1 and X2

Acc to question X1 : X2 = 7 : 5 i,e X1\X2 = 7/5 => X1= (7/5)*X2 =1.4*X2..........Eq1

(X1-40)/(X2-40) = 27/17 .....Eq2

Putting Eq1 in Eq2

(1.4*X2 - 40) / (X2-40) = 27/17

=> (1.4*X2 - 40) *17 = 27* (X2-40)

=> 23.8*X2 - 680 = 27 X2-1080

=> 3.2*X2 = 400

=> X2=125 .....Eq3

Put value of X2 in Eq1

X1= 1.4*X2

X1= 1.4*125

X1=175

ie sum of two numbers X1+X2=125+175=300

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