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# LRDI sets (Elementary) 16

When Ram will be as old as Ram's father is now, Ram will be five times as old as Ram's son is now. But at that time Ram's son will be eight years older than Ram is now. At present, the sum of the ages of Ram's father and Ram is 100 years.

Q1. How old is Ram's son?

1. 8 years
2. 13 years
3. 16 years
4. 19 years

Q2. How old would Ram have been 5 years ago?

1. 30 years
2. 33 years
3. 38 years
4. 45 years

Q3. After 10 years, how old will Ram's father be?

1. 56 years
2. 65 years
3. 75 years
4. 66 years

Explanation:

Let the present age of Ram = x years. The present age of his son = y years. The present age of Ram's father = z years. By the question, x + z = 100 x = 100 - z ...(i)

Again, z = 5y ...(ii)

and y + (z - x) = x + 8 y + z = 2x + 8.

Putting the value of x from equation (i) we get,

y + z = 2 (100 - z) + 8 y + 3z = 208. Putting the value of z from equation (ii) we get,

y + 3(5y) = 208 = 16y = 208. y = 13, from equation (ii), z = 65 and from (i) x = 35.

Q1. Age of son = 13 years. Ans.(2)

Q2. Age of Ram 5 years ago = 35 - 5 = 30 years. Ans.(1)

Q3. After 10 years, age of Ram's father = 65 + 10 = 75 years. Ans.(3)

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