**Tips and tricks to solve age problems**– Hello friends, once again I welcome all of you for another most important Math trick explanation. This Math trick will help you in the preparation of SSC CGL, RRB, RRB NTPC, UPSC & SSC GD Exams. Its name is **Tips and tricks to solve age problems**

## Problems on Ages Shortcuts Tricks

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**Case-1**

If Present age = x years(Given)

Then,

Age ago ‘n’ years = (x-n) years

Age after ‘m’ years = (x+m) years

**Case-2**

If Age ago ‘n’ years = x years(Given)

Then,

Present age = (x+n) years

Age after ‘m’ years = (x+n+m) years

**Case-3**

If Age after ‘n’ years = x years(Given)

Then,

Present age = (x-n) years

Age ago ‘m’ years = (x-n-m) years

## Age Problem tricks, Concepts and Examples Type-1

**(1)**The ratio of ages of two persons is 4:7 and the age of one of them is greater than that of the other by 30 years. The sum of their ages is

(a)110 (b)100 (c)70 (d)40

**Solution:**

Now,

3 unit = 30 years

1 unit =30/3 =10 years

Present age of two persons are respectively=40 and 70 years

Sum of their age=40+70=110 years ans.

**(2)**Two years ago, A was four times as old as B. 8 years hence, A’s age will exceed B’s age by 12 years. The ratio of the present ages of A and B is.

(a)5:1 (b)3:1 (c)4:1 (d)3:2

**Solution:**

Now,

3 unit = 12 years

1 unit = 4 years

2 years ago, Age of A=16 years

2 years ago, Age of B=4 years

Present age of A=16+2=18 years

Present age of B=4+2=6 years

Ratio = 18/6 =3:1 Ans.

**(3)**The ratio between Sumit’s and Prakash’s age at present is 2:3. Sumit is 6 years younger than Prakash. The ratio of Sumit’s age to Prakash’s age after 6 years will be.

(a)2:3 (b)1:2 (c)4:3 (d)3:4

**Solution:**

Now,

1 unit = 6 years

Present age of Sumit’s = 12 years

Present age of Prakash’s = 18 years

After 6 years, age of Sumit’s = (12+6)=18 years

After 6 years, age of Prakash’s = (18+6)=24 years

Ratio=18/24 = 3:4 Ans.

**(4)**Ratio of Ram’s age to Mohan’s age is 4:3. Ram will 26 years old after 6 years. Then the present age of Mohan is.

(a)18 years (b)21 years (c)15 years (d)24 years

**Solution:**

Present age of Ram=26-6=20 years

4 unit=20 Years

1 unit=5 years

Present age of Mohan=3 unit=15 Years Ans.

**(5)**Raja was twice as old as Ajay 10 years back. How old is Ajay today, if Raja will be 40 years old 10 years hence?

(a)10 years (b)15 years (c)20 years (d)30 years

**Solution:**

10 years ago, age of Raja = (40-10-10)=20 years

Now,

2 unit = 20 years

1 unit = 10 years

10 years ago, age of Ajay=1 unit =10 years

Present age of Ajay = (10+10)years=20 years Ans.

## Age Problem tricks, Concepts and Examples Type-2

**(1)**The ratio of the age of a father to that of his son is 5:2. If the product of their ages in years is 1000. Then the father’s age after 10 years will be:

(a)50 years (b)60 years (c)80 years (d)100 years

**Solution:**

5x × 2x =1000

x^{2} = 100

x = 10

Present age of father = 50 years

Present age of son = 20 years

After 10 years,

Age of Father = (50+10)Years

= 60 Years Ans.

**(2)**The ratio of the father’s ages to the son’s age is 4:1. The product of their ages is 196. What will be the ratio of their ages after 5 years?**
**(a)11 : 3 (b)11 : 4 (c)12 : 4 (d)12 : 3

**Solution:**

4x × x =196

x^{2} = 49

x = 7

Present age of father = 28 years

Present age of son = 7 years

After 5 years,

Age of Father = (28+5)Years

= 33 Years

Age of Son = (7+5) years

= 12 years

Ratio = 33/12 =11:4 Ans

## Age Problem tricks, Concepts and Examples Type-3

**(1)**At present, the ratio of the age of Maya and Chhaya is 6:5 and fifteen years from now, the ratio will get changed to 9:8. Maya’s present age is.

(a)21 years (b)24 years (c)30 years (d)40 years

**Solution:**

Now,

3 unit = 15 years

1 unit = 5 years

so, Present age of Maya’s = 30 years Ans.

**(2)**Eighteen years ago, the ratio of A’s age to B’s age was 8:13. Their present ratios are 5:7. What is the present age of A?

(a)60 years (b)70 years (c)50 years (d)40 years

**Solution:**

Now,

9 unit = 90 years

1 unit = 10 years

So, present age of A = 50 years Ans.

**(3)**The ratio of present age of two brothers is 1:2 and 5 years back. The ratio was 1:3. what will be the ratio of their age after 5 years?

(a)1:4 (b)2:3 (c)3:5 (d)5:6

**Solution:**

Now,

1 unit = 10 years

Present age of both brothers= 10 and 20 years

After 5 years,

Age of 1st brother=10+5=15 years

Age of 2nd brother=20+5=25 years

Ratio=15/25 =3:5 Ans.

**(4)**At present age of father is three times the age of his son. Four years hence the ratio between the ages of father and son becomes 13:5 respectively. what is the present age of father?

(a)52 years (b)65 years (c)48 years (d)42 years

**Solution:**

Now,

2 unit = 32 years

1 unit = 16 years

So, present age of father = 48 years Ans.

**(5)**The age of man is 4 times that of his son. 5 years ago, the man was nine times as old as his son was at that time. What is present age of the man?

(a)36 years (b)34 years (c)28 years (d)32 years

**Solution:**

Now,

5 unit = 40 years

1 unit = 8 years

So, present age of Person = 32 years Ans.

## Age Problem tricks, Concepts and Examples Type-4

**(1)**Harsha is 40 years old and Ritu is 60 years old. How many years ago was the ratio of their ages 3:5?**
**(a)10 years (b)20 years (c)37 years (d)5 years

**Solution:**

Now,

2n = 20

n = 10 years Ans.

**(2)**The present age of two persons are 36 and 50 years respectively. If after n years the ratio of their age will be 3:4, then the value of n is.**
**(a)4 (b)7 (c)6 (d)3

**Solution:**

So, n=6 years Ans.

### Age Problem tricks, Concepts and Examples Type-5

(1)The ratio of the age of Ram and Rahim 10 years ago was 1:3. The ratio of their age five years hence will be 2:3. Then the ratio of their present age is.

(a)1:2 (b)3:5 (c)3:4 (d)2:5

Solution:

Now,

3 unit = 15 years

1 unit = 5 years

10 years ago,

Age of Ram= 5 years

Age of Rahim = 15 years

Present age of Ram = 5+10=15 years

Present age of Rahim = 15+10=25 years

Ratio= 15/25 =3:5 Ans.

**(2)**The Ratio of the ages of a father and his son 10 years hence will be 5:3, while 10 years ago, it was 3:1. The ratio of the age of the son to that of the father today is

(a)1:2 (b)3:1 (c)2:3 (d)2:5

**Solution:**

Now,

4 unit = 40 years

1 unit = 10 years

10 years after,

Age of father = 50 years

Age of son = 30 years

Present age of father = 50-10=40 years

Present age of son = 30-10 =20 years

Ratio= 20/40=1:2 Ans.

**(3)**Three years earlier the father was 7 times as old as his son. Three years hence the father’s age would be four times that of his son. What are the present ages of father and son (in years)?

(a)45, 9 (b)55, 11 (c)45, 11 (d)25, 7

**Solution-**

Now,

3 unit = 18 years

1 unit = 6 years

3 years ago,

Age of father and son = 42 and 6 years

Present age of father = 42 +3 = 45 years

Present age of son = 6+3 = 9 years

### Age Problem tricks, Concepts and Examples Type-6

(1)The ratio of Ram’s age and Shyam’s age is 3:5 and sum of their ages is 80 years. The ratio of their ages after 10 years will be:

(a)3:5 (b)3:2 (c)2:3 (d)1:2

**Solution:**

Sum of present age = 80 years

8 unit(i.e 3+5) = 80 years

1 unit = 10 years

Present age of Ram and Shyam = 30 and 50 years

**After 10 years,**

Age of Ram = 30+10 = 40 years

Age of Shyam = 50+10 = 60 years

Ratio=40/60 =2:3

**(2)**Five years ago, the sum of the ages of father and son was 60 years. The ratio of their present ages is 4:1. The present age of the father is:

(a)61 years (b)56 years (c)48 years (d)51 years

**Solution:**

Sum of ages ago 5 years = 60 years

Sum of Present age = 60+5+5=70 years

Now,

5 unit(i.e 4+1) = 70 years

1 unit = 14 years

So present age of father=56 years

**(3)**The sum of the age of a father and his son is 100 years now. 5 years ago their age were in the ratio of 2:1. The ratio of the age of father and son after 10 years will be.**
**(a)5:3 (b)4:3 (c)10:7 (d)3:5

**Solution:**

Sum of present age of father and son =100 years

Sum of age ago 5 years = 100-5-5=90 years

Now,

3 unit (i.e 2+1)= 90 years

1 unit =30 years

5 years ago, age of father and son=60 and 30 years

difference of time=5+10=15 years

After 10 years

Age of father=60+15=75 years

Age of Son =30+15 45 years

Ratio= 75/45=5:3 Ans

**(4)**The sum of the ages of a mother and her daughter is 50 years. Also 5 years ago, the mother’s age was 7 times the age of the daughter. What are the present age of the mother and the daughter (in years).

(a)40, 10 (b)36, 9 (c)48, 12 (d)32, 8

**Solution:**

Sum of present age of mother and doughter=50 years

Sum of the age ago 5 years=50-5-5=40 years

Now,

8 unit (i.e 7+1)= 40 years

1 unit =5 years

5 years ago,

Age of Mother and daughter=35 and 5 years

Present age of Mother=35+5=40 years

Present age of Daughter=5+5 =10 years

**(5)**The sum of the ages of a son and father is 56 years after 4 years, the age of the father will be three times that of the son. What is the age of the son?

(a)14 years (b)12 years (c)8 years (d)10 years

**Solution:**

Sum of Present age of son and father=56 years

Sum of age 4 years after = 56+4+4=66 years

Now,

4 unit (i.e 3+1)= 64 years

1 unit =16 years

4 years after,

Age of father = 48 years

Age of son = 16 years

Present age of father=48-4=42 years

Present age of son = 16-4=12 years

**(6)**At present, the sum of the ages of A, B and C is 150 years, whereas 10 years ago, the ratio of their age was 5:4:3. Find the ratio of their ages 10 years hence.

(a)7:5:3 (b)6:9:5 (c)4:3:5 (d)7:6:5

**Solution:**

Sum of present age of A, B and C = 150 years

10 years Ago, Sum of age of A, B and C =120 years

Now,

12 unit(5+4+3)=120 years

1 unit=10 years

10 years Ago, age of A, B and C=50, 40 and 30 years

Difference of time=10+10=20 years

10 years after,

Age of A = 50+20=70

Age of B = 40+20=60

Age of C = 30+20=50

Ratio=7:6:5 Ans

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