MCQ: Problem Based on Ages - 3 - SSC CGL MCQ

# MCQ: Problem Based on Ages - 3 - SSC CGL MCQ

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## 15 Questions MCQ Test - MCQ: Problem Based on Ages - 3

MCQ: Problem Based on Ages - 3 for SSC CGL 2024 is part of SSC CGL preparation. The MCQ: Problem Based on Ages - 3 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Problem Based on Ages - 3 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Problem Based on Ages - 3 below.
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MCQ: Problem Based on Ages - 3 - Question 1

### 8 years ago, the ratio of the age of P to that of Q was 6 : 7 which is equal to the ratio of the present age of A to that of B. 6 years later, A will be 1.2 times as old P and B will be 13 years older than Q. What is the present age (in years) of Q?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 1

Let the present age of A = 6x and B = 7x
8 years ago:
(Ratio of the age of P : Q = 6 : 7
Let the age of P = 6y and Q = 7y)
Present age of P = 6y + 8 and that of Q = 7y + 8
6 years later:
(6x + 6) : (6y + 8 + 6) = 6 : 5
and 7x – (7y + 8) = 13
Solving the above equations, we get:
x = 9 and y = 6
Present age of Q = 7y + 8 = 50 years
Hence, option A is correct.

MCQ: Problem Based on Ages - 3 - Question 2

### In the last 6 years, the age of A increased by 25% and in the next 8 years age of B will increase by 20%. 15 years from now, the ratio of the age of A to that of B, will be the same as the ratio of the age of C to that of D. If the difference between the age of C and D is 6 years, what is the present age (in years) of D?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 2

After 15 years, ratio of the age of A : B = (30 + 15) : (40 + 15) = 9 : 11
After 15 years, ratio of the age of C : D = 9 : 11 and the difference between their age = 6
After 15 years, age of C = 27 and D = 33
Present age of D = 33 – 15 = 18 years
Hence, option D is correct.

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MCQ: Problem Based on Ages - 3 - Question 3

### The difference between the square of the present age (in years) of a mother and her daughter is 875. 5 years later, the ratio of their ages will be 7 : 2. What is the present age (in years) of the mother?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 3

After 5 years, ratio of the age of Mother : Daughter = 7 : 2
Let the present age of Mother = 7x – 5 and Daughter = 2x – 5
(7x – 5)2 – (2x – 5)2 = 875
49x2 + 25 −70x – 4x2 – 25 + 20x = 875
45x2 – 50x – 875 = 0
9x2 – 10x – 175 = 0
9x2 – 45x + 35x – 175 = 0
x = 5
Present age of Mother = 7x – 5 = 30 years
Daughter = 2x – 5 = 5 years
Hence, option A is correct.

MCQ: Problem Based on Ages - 3 - Question 4

The average age of a family of four members (father, mother, boy and girl) is 28 years and when it becomes 32 years the girl will be 10 years old. When the girl was born the father was four times as old as the boy. If the father is 2 years older than the wife, what is the present age (in years) of the boy?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 4

Present age of girl = 10 – (32 – 28) = 6 years
Girl was born 6 years ago, at that time:
Let the age of boy = x and age of the father = 4x
So, age of Wife = 4x − 2
The average age of the family 6 years ago = 28 – 6 = 22
x + 4x + 4x – 2 = 4 × 22
x = 10
Present age of the boy = x + 6 = 16 years
Hence, option D is correct.

MCQ: Problem Based on Ages - 3 - Question 5

The age gap between Amit and Kiran is 4 years and that between Kiran and Rashi is also 4 years. The product of the age of Amit and Rashi is 240 years. If all of them have different ages, which of the following can be the ratio of the age of Amit to that of Kiran?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 5

Either Amit > Kiran > Rashi or Rashi > Kiran > Amit
Let the ages be (x – 4), x and (x + 4)
(x − 4) × (x + 4) = 240
x = 16
x – 4 = 12 and x + 4 = 20
Ratio of the age of Amit : Kiran = 12 : 16 = 3 : 4
or
20 : 16 = 5 : 4
Hence, option B is correct.

MCQ: Problem Based on Ages - 3 - Question 6

The average ages of A and B is 157.14% of the average age of C and D. 10 years ago, the ages of A, B, C and D were ‘X + 12’ years, ‘X + 16’ years, ‘X + 2’ years and ‘X − 6’ years, respectively. What is the present average age (in years) of A and D?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 6

(A + B) : (C + D) = 11 : 7
(X + 12 + X + 16 + 20) : (X + 2 + X – 6 + 20) = 11 : 7
X = 20
10 years ago age of A = 32, B = 36, C = 22 and D = 14
Present age of A = 42, B = 46, C = 32 and D = 24
Present average age of A and D

Hence, option C is correct.

MCQ: Problem Based on Ages - 3 - Question 7

A family has six members and 12 years ago their average age was 50 years. 4 years ago, they married their only daughter and this year they married their only son so this year family again has six members including daughter-in-law and excluding the daughter such that the sum of the age of all family members is 382 years. What is the age difference between the daughter and the daughter-in-law?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 7

Total age 12 years ago = 6 × 50 = 300
Presently total age would have been = 300 + 6 × 12 = 372
Present total age = 382 years
The difference is because of the substitution of Daughter with Daughter in law
So, the age difference between them = 382 – 372 = 10 years
Hence, option C is correct.

MCQ: Problem Based on Ages - 3 - Question 8

Firdauz, Ali, Sarfaraz, Sameer and Faiz are five brothers, youngest to eldest in the same order. The age gap between the five brothers is equal such that the ratio of the age of the youngest to the eldest brother is 5 : 9. Ali will be ‘z’ years old when the ratio of the age of Firdauz to the age of Faiz becomes 9 : 13. Present age of Sameer is what percent of ‘z’?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 8

Firdauz, Ali, Sarfaraz, Sameer and Faiz
Faiz : Firdauz = 9 : 5
Let Faiz = 9x, Sameer = 8x, Sarfaraz = 7x, Ali = 6x and Firdauz = 5x
After ‘k’ years ratio of the age of Firdauz : Faiz = 9 : 13
(5x + k) : (9x + k) = 9 : 13
k = 4x
Age of Ali after k years,
z = 6x + 4x = 10x

Hence, option D is correct.

MCQ: Problem Based on Ages - 3 - Question 9

Rohan is 8 times as old as Jatin and 6 years later he will be 3.5 times as old as Rekha. Rekha celebrated her 8th birthday 1 year after Jatin celebrated his first birthday. What is the present age (in years) of Rekha?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 9

At present let the age of
Jatin = x and Rohan = 8x
6 years later: Rohan = 8x + 6

Jatin = x + 6
Age difference between Jatin and Rekha = 8 – 2 = 6

16x + 12 = 7x + 84
9x = 72
x = 8

Hence, option C is correct.

MCQ: Problem Based on Ages - 3 - Question 10

The ratio of the age of A to that of B ‘x’ years ago was 2 : 3 and this ratio will be 7 : 8 after ‘3x’ years. Presently B is 17/13 times as old as A. 2 years after A was born, B was five times as old as A. What is the value of ‘x’?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 10

When Age of A = 2 years
Age of B = 2 × 5 = 10 years
Presently the ratio of their age is 13 : 17
As the age difference between them is 8 years
The present age of A = 26 years and B = 34 years
(26 – x) : (34 – x) = 2 : 3
x = 10
Hence, option D is correct.

MCQ: Problem Based on Ages - 3 - Question 11

The sum of the ages of Chetan and Ravi is equal to the age of their grandmother. 8 years ago, Ravi was 1/4 times as old as his grandmother’s present age and 4 years later he will be 3/8 times as old as her present age. What will be the ratio of the age of Ravi to that of Chetan after 8 years?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 11

Let the age of the grandmother = 8x

Difference = 3x – 2x = (8 + 4)
x = 12
Age of Grandmother = 8 × 12 = 96 years
Age of Ravi = 2x + 8 = 32 years
Age of Chetan = 96 – 32 = 64 years
Reqd. ratio = (32 + 8) : (64 + 8) = 40 : 72 = 5 : 9
Hence, option C is correct.

MCQ: Problem Based on Ages - 3 - Question 12

Sneha and Garima met at a Coffee shop where Garima told Sneha, “10 years ago I was 2/3rd of your age and 14 years later you will be 7/6th of my age.” If both of them completed their high school at the age of 16, what was the age (in years) of Garima when Sneha completed her high school?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 12

Let the present age of Garima = G and Sneha = S
(G − 10) : (S − 10) = 2 : 3
(G + 14) : (S + 14) = 6 : 7
Solving we get:
G = 22 and S = 28
Both of them completed high school at the age of 16 years.
As Garima is 6 years younger to Sneha
When Sneha was 16 years old
Age of Garima = 16 – 6 = 10 years
Hence, option B is correct.

MCQ: Problem Based on Ages - 3 - Question 13

The average age of Naira, Ada and Sehar is 35 years. When Ada becomes as old as the present age of Naira, Naira’s age will be 11/6 times the present age of Sehar. 12 years ago Sehar was as old as the present age of Ada. What is the age (in years) of the oldest among them?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 13

12 years ago Sehar was as old as Ada at present
So, Sehar is 12 years elder to Ada
Let the present age of Naira = N, Sehar = 6x and Ada = 6x – 12
When age of Ada becomes = N, Age of Naira = 11x
11x – N = N – (6x – 12)
N = 8.5x – 6
Sum of ages of all = 3 × 35
8.5x – 6 + 6x + 6x – 12 = 105
x = 6
Present age of Naira = 8.5x – 6 = 45
Ada = 24 and Sehar = 36
Age of the oldest one among them = 45 years
Hence, option C is correct.

MCQ: Problem Based on Ages - 3 - Question 14

15 years from now A will be thrice as old as B was 5 years ago. C is 2/5 times as old as the present average age of A and B. If the present average age of A, B and C is 20 years, what was the age (in years) of A when C was born?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 14

A + B + C = 3 × 20 = 60

C : (A + B) = 1 : 5
So, C = 10 and A + B = 50
A + 15 = 3(B – 5)
3B = A + 30
and A + B = 50
Solving we get B = 20 and A = 30
When C was born age of A was = 30 – 10 = 20 years
Hence, option A is correct.

MCQ: Problem Based on Ages - 3 - Question 15

A couple got married when both of them were 20 years old. After ‘x’ years a son was born and ‘y’ years later they had twin daughters. Presently the total age of the family is 116 years and the youngest member is 10 years old. If the ratio of the age of the mother and the son is 5 : 2, what is the present age (in years) of the son?

Detailed Solution for MCQ: Problem Based on Ages - 3 - Question 15

Couple got married at the age of 20, x years later a boy was born, y years later two girls were born and each girl is aged 10 years presently
Age of boy = y + 10
Age of the couple = 20 + x + y + 10 = 30 + x + y
(30 + x + y) : (y + 10) = 5 : 2
10 + 2x = 3y -------------- (1)
2(30 + x + y) + y + 10 + 2 × 10 = 116
2x + 3y = 26 --------------- (2)
Solving equations (1) and (2) we get:
x = 4 and y = 6
Present age of the boy = y + 10 = 16 years
Hence, option D is correct.

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