Tez Singh recently joined a new school. On the first day, his class teacher asked his age. Tez, being a cheeky boy, replied: “Ma’am, when I was born, my sister Ananti was one-quarter the age of our mother, and presently she is one-third the age of my father”. The teacher, a little flustered, said “I want your age, not the age of your family members”. Tez singh, in his inimical style, replied, “I am one-fourth of my mother’s present age, and in four years, i will be one-fourth the age of my father. Now Ma’am, if you are a real maths teacher, you should be able to figure out my precise age”. Was the teacher able to guess the age, and in case she was, what is Tez Singh’s age?

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Explanation: The equations that help us solve this riddle are as follows:

(The following is list of notations followed to solve the puzzle: A=Anant’s age at year 0 M=Mom’s age at year 0 D=Dad’s age at year 0 T=Tez Singh’s age today,

The problem gives us the following equations:

Ananti is 1/4 her mother’s age at T=0 A = 1/4*M……………………………………1 Presently, Ananti’s age (A+T) is 1/3 her father’s age (D+T) A+T = 1/3*(D+T)…………………………….2 Presently, Tez’s age (T) is 1/4 his mother’s age (M+T) T = 1/4*(M+T)………………………………….3 In 4 years, Tez’s age (T+4) will be 1/4 that of his father’s age (D+T+4)

T+4 = 1/4*(D+T+4)……………………………….4

Now we have T+4 =1/4*(D+T+4)

T+4=(D+T+4)/4 T= {(D+T+4)/4}-4 T=(D+T-12)/4…………………………………5

From 5 and 3 (if L.H.S. is equal then R.H.S. side is also equal)

(D+T-12)/4 = ¼ (M+T)

D = M+12……………………………………..6

From 3, M= 3T

So, D= 3T+12………………………………….7

Putting the value of M in 1, we have A = ¾T……………………………8

From eq. 2 A+T= D/3 +T/3 3A+3T=D+T 3A= D+T-3T

Put value of D from 7in this: 3A= 3T+12+T-3T A=(T+12)/3………………………………………9 From 8 and 9 3/4T= (T+12)/3 By solving T= 9.6

Now we solve these last 2 equations for M & D respectively, and substitute into the first 2 equations will result in 2 equations in terms of A & T: A = 3/4*T A = 1/3*(T+3T+12)

Solving for T = 9.6 years Tez Singh’s age must have been nine years and three-fifths.

Solution please