Problems ON AGE Questions FOR Bank Exams with Detailed Solutions

​$$\text{Given:}\\\text{Five years ago } A:B = 3:4\\\text{After five years } A:B = 5:6\\[6pt]\text{Concept Used:}\\\text{Age problems using ratio method}\\[6pt]\text{Formula Used:}\\\text{Ratio} = \frac{\text{Age of A}}{\text{Age of B}}\\[6pt]\text{Solution:}\\\text{Let ages 5 years ago be } 3x \text{ and } 4x\\\text{After 5 years: } 3x+10,\;4x+10\\[6pt]\frac{3x+10}{4x+10} = \frac{5}{6}\\[6pt]6(3x+10) = 5(4x+10)\\18x + 60 = 20x + 50\\2x = 10\\x = 5\\[6pt]\text{Present age of B} = 4x + 5 = 25\\[6pt]\text{Final Answer:}\\\boxed{25 \text{ years}}$$

​​Exam Hall Approach

​$$\textbf{Given:}\\\text{Five years ago, } S-5 = 3(P-5)\\\frac{P+6}{S+10} = \frac{1}{2}\\[6pt]\textbf{Concept Used:}\\\text{Linear equations in ages}\\[6pt]\textbf{Formula Used:}\\\text{Future age} = \text{Present age} + \text{Years}\\\text{Past age} = \text{Present age} - \text{Years}\\[6pt]\textbf{Solution:}\\S - 5 = 3(P - 5)\\S = 3P - 10\\2(P + 6) = S + 10\\S = 2P + 2\\3P - 10 = 2P + 2\\P = 12\\S = 26\\\text{S age three years ago} = 26 - 3 = 23\\[6pt]\textbf{Final Answer:}\\\boxed{23}$$

Exam Hall Method:

​$$\text{Given} \\\text{Presentiya's present age} = R \\\text{Asha's present age} = A \\\text{Concept Used} \\\text{Linear equations based on age relations and ratios} \\\text{Formula Used} \\\text{Percentage increase} = \left(1 + \frac{p}{100}\right)\times \text{Value} \\\text{Ratio} = \frac{a}{b} \\\text{Solution} \\R + 20 = 1.6(A + 10) \\(R - 10):(A - 20) = 5:2 \\\frac{R - 10}{A - 20} = \frac{5}{2} \\2(R - 10) = 5(A - 20) \\2R - 20 = 5A - 100 \\2R = 5A - 80 \\R = \frac{5A - 80}{2} \\R + 20 = 1.6A + 16 \\R = 1.6A - 4 \\1.6A - 4 = \frac{5A - 80}{2} \\3.2A - 8 = 5A - 80 \\1.8A = 72 \\A = 40 \\R = 60 \\\text{Required sum} = 40 + (60 + 5) = 105 \\\text{Final Answer} \\105$$

Exam Hall Method:

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Let present age of R = r Let present age of S = s
Given: r + s = 60 ...(1)
S is 16 years younger than R
So, s = r - 16 ...(2)
Substitute (2) into (1):
r + (r - 16) = 60
2r - 16 = 60
2r = 76
r = 38
Now, s = 38 - 16 = 22
Age of T = 1.5 × R
T = 1.5 × 38 = 57
Now, Sum of R + S + T = 38 + 22 + 57 = 117

Let present age of father = F
Let present age of A = a Let present age of B = b
Given: A = 20% of father’s age 15 years ago
So, a = 0.2(F - 15) ...(1)
B = 60% of father’s age 10 years ago
So, b = 0.6(F - 10) ...(2)
Now, a + b = 31
Substitute (1) and (2):
0.2(F - 15) + 0.6(F - 10) = 31
0.2F - 3 + 0.6F - 6 = 31
0.8F - 9 = 31
0.8F = 40
F = 50

Exam Hall Method: 

Given:

The average age of five employee of a company = 54 yrs (three years ago).

The present average age = 52 yr (after the inclusion of a new employee). 

Explanation:

Total present age of five employee

= 54 × 5 + 3 × 5 = 270 + 15 = 285 years
Total present age of all six employee = 52 × 6 = 312
Age of new employee = 312 – 285 = 27 years

Exam Hall Method: 

Information:
The age of Raju two years ago = 75% of Rita’s age at that time.
After two years, Rita’s age will be 33 1/3% of her father’s age.
Average age of Rita’s father and mother = 31 yrs
Rita’s mother’s age =28 yrs
Explanation:
Rita’s father’s age = 31 × 2 – 28
= 34 yrs
Rita’s age after two yr =100/300×(36)
= 12 yr
∴ Rita’s present age = 10 yr
∴ Raju’s present age =(10-2)×75/100+2
= 8 yr

Exam Hall Method: 

Information: 

Ratio of ages of Ravi and Shusma =  5 : 3 (three years ago)

Ratio of ages of Ravi and Shusma =   4 : 3 (2 years hence)

Explanation:

Let three years before,

Ravi’s age = 5x
Shusma’s age = 3x
A/q,
(5x+5)/(3x+5)=4/3
=> 15x + 15 = 12x + 20
=> x =5/3
∴ Present age of Ravi =5×5/3+3
=34/3 yrs
= 11 yrs 4 months 

Exam Hall Method: 

Information Given:
Suresh's present age = 6 × (his son's present age)
13 years later, ratio of their ages = 11 : 4
Asked: Suresh’s present age
Explanation:
Let son’s present age = x, so Suresh’s age = 6x
After 13 years:
Suresh’s age = 6x + 13
Son’s age = x + 13
Given $$\frac{6x + 13}{x + 13} = \frac{11}{4}$$​
Cross-multiply:
4 × (6x + 13) = 11 × (x + 13)
24x + 52 = 11x + 143
24x - 11x = 143 - 52
13x = 91
x = $$\frac{91}{13} = 7$$​
So, Suresh's present age = 6 × 7 = 42 years

Exam Hall Approach

Information Given:
Sum of ages of F and S = 45 years
Five years ago, F's age = 35 years
Asked: S's age 4 years hence
Explanation:
F's present age = 35 + 5 = 40 years
S's present age = 45 - 40 = 5 years
S's age 4 years hence = 5 + 4 = 9 years

Exam Hall Approach

Information Given:

Present age of Gopal is 12 years more than the present age of Ram.
After 2 years, the ratio of Ram’s age to Gopal’s age will be 1:2.
Concept/Formula Used:
Let present age of Ram = x years
Present age of Gopal = x + 12 years
Age after 2 years: Ram = x + 2, Gopal = x + 12 + 2 = x + 14
Ratio after 2 years: (x + 2) : (x + 14) = 1 : 2
Explanation:
Using the ratio condition:
(x + 2) / (x + 14) = 1 / 2
Cross-multiply:
2(x + 2) = 1(x + 14)
2x + 4 = x + 14
2x - x = 14 - 4
x = 10
Therefore,
Present age of Ram = 10 years
Present age of Gopal = x + 12 = 10 + 12 = 22 years

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Information Given:
Eight years ago, the ages of Ramesh and Suresh were (y-4) years and (y+2) years respectively.
The ratio of present ages of Ramesh and Suresh is 7:8 respectively.
Basic Explanation:
ATQ,
$$\frac{y - 4 + 8}{y + 2 + 8} = \frac{7}{8}$$​
$$\frac{y + 4}{y + 10} = \frac{7}{8}$$​
8y + 32 = 7y + 70
y = 38
Required answer = 3(38)+5=119