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1. The age of mother and daughter are inthe ratio 9:4. Five years ago, age ofmother was 10 years more than twicethe age of her daughter. Find theirpresent ages.(CBSE 2014)

Answer»

Let x and y be the present age of mother and daughter

we have,x/y = 9/4=> x = 9y/4 -- (1)

from the given condition we get,x-5 = 10 + 2(y-5)=> x-5 = 10+ 2y-10=> (9y/4) - 5 = 2y=> (9y/4) - 2y = 5=> (9y - 8y)/4 = 5=> y/4 = 5=> y = 20putting y = 20 in (1)x = (9×20)/4=> x = 45

therefore the present ages of the mother and the daughter are 45 years and 20 years

let present age of mother be 9x daughter 4x5years ago mother age = 9x-5daughter. = 4x-59x-5= 2(4x-5)+109x-5=8x-10+109x-8x=5x=5so mother age =9x= 9×5=45daughter age=4x=4×5 =20 years



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