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All questions of Problem on Ages for UPSC CSE Exam

Ravi is now 4 years older than Emma and half of that amount older than Ishu. If in 2 years, Ravi will be twice as old as Emma, then in 2 years what would be Ravi’s age multiplied by Ishu’s age?
  • a)
    68
  • b)
    28
  • c)
    48
  • d)
    50
  • e)
    52
Correct answer is option 'C'. Can you explain this answer?

Anaya Patel answered
Ravi – x + 4
Emma – x
Ishu – x + 2
(Ravi 4 years older than Emma & 2 years older than Ishu)
Ages after 2 yrs
Ravi – x + 6
Emma – x + 2
Ishu – x + 4
x+6 = 2(x + 2)
x = 2
Ravi * Ishu = 8 * 6 = 48

Jack is now twice as old as Femina, who is two years older than Suresh. Four years ago, Jack was four times as old as Suresh. How old is Jack now?
  • a)
    18
  • b)
    12
  • c)
    16
  • d)
    20
  • e)
    24
Correct answer is option 'D'. Can you explain this answer?

Kishan Singh answered
Let the age of SURESH = X
age of FEMINA = X + 2
age of JACK = 2 ( X + 2 ) = 2X +4

four years ago,
JACK age =( 2X +4 )- 4 = 2X
SURESH age = X - 4

A/Q -
2X = 4 ( X - 4 )
=> X = 8
JACK present age = 2 (X +2)= 20 year . option( D)

Out of the three annual examinations, each with a total of 500 marks, a student secured average marks of 45% and 55% in the first and second annual examinations. To have an overall average of 60%, how many marks does the student need to secure in the third annual examination ?
  • a)
    450
  • b)
    400
  • c)
    350
  • d)
    300
  • e)
    None of the Above
Correct answer is option 'B'. Can you explain this answer?

Rhea Reddy answered
Total marks for three examinations = 3x 500 = 1500
Total required marks in three examinations = 60% of 1500
= (3 x 500 x 60) / 100
= 900
Marks secured in first examination = 45 % of 500
= (500 x 45) / 100
= 225
Marks secured in third examination = 55 % of 500
= (500 x 55) / 100
= 275
Thus, the required marks in third examination
= 900 – (225 + 275)
= 900 – 500
= 400

Arun will be half as old as Lilly in 3 years. Arun will also be one-third as old as James in 5 years. If James is 15 years older than Lilly, how old is Arun?
  • a)
    6
  • b)
    8
  • c)
    9
  • d)
    5
  • e)
    4
Correct answer is option 'B'. Can you explain this answer?

Aisha Gupta answered
let age of Arun =x, Lilly =y James = z
(x+3) =1/2 *(y+3) so we have 2x-y =-3 -(1)
(x+5) =1/3 * (z+5) ; ⇒ 3x-z=-10 -(2)
From (1)&(2) we get, x+y-z =-7 -(3)
we have z =15+y – (4)
from equation 3 and 4 we get x=8

The average weight of the students in four sections Red, Black, Green and Yellow is 60 kg. The average weight of the students of Red, Black, Green and Yellow individually are 45 kg, 50 kg, 72 kg and 80 kg, respectively. If the average weight of the students of section Red and Black together is 48 kg and that of Black and Green together is 60 kg. What is the ratio of the number of the students in sections Red and Yellow?
  • a)
    12 : 7
  • b)
    2 : 3
  • c)
    4 : 3
  • d)
    8 : 5
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Faizan Khan answered
Average weight of students of sections of Red and Black = 48 kg
⇒ (45a + 50b)/(a + b) = 48
⇒ 15a = 10b
Average weight of students of sections of Black and Green = 60 kg
⇒ 50b + 72c = 60(b + c)
⇒ 10b = 12c
Average weight of students of Red, Black, Green and Yellow = 60 kg
45a + 50b + 72c + 80d = 60(a + b + c + d)
⇒ 15a + 10b – 12c – 20d = 0
⇒ 15a = 20d
⇒ a : d = 4 : 3

The average weight of 4 persons, Amit, Bala, Catherine and David is 65 kg. The 5th person Elina is included and the average weight decreses by 2 kg. Amit is replaced by Francis. The weight of Francis is 4 kg more than Elina. Average weight decreases because of the replacement of Amit and now the average weight is 64 kg. Find the weight of Amit.
  • a)
    54 kg
  • b)
    66 kg
  • c)
    55 kg
  • d)
    68 kg
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Sagar Sharma answered
Given Information
- Average weight of Amit, Bala, Catherine, and David = 65 kg
- Number of persons = 4
- Total weight of Amit, Bala, Catherine, and David = 65 * 4 = 260 kg
Introducing Elina
- When Elina is included, the average weight decreases by 2 kg.
- New average weight = 65 kg - 2 kg = 63 kg
- Total weight of 5 persons (Amit, Bala, Catherine, David, Elina) = 63 * 5 = 315 kg
Calculating Elina's Weight
- Total weight of Amit, Bala, Catherine, and David = 260 kg
- Total weight of all 5 persons = 315 kg
- Weight of Elina = 315 kg - 260 kg = 55 kg
Replacing Amit with Francis
- Francis's weight = Elina's weight + 4 kg = 55 kg + 4 kg = 59 kg
- New total weight after replacing Amit = 260 kg - Amit's weight + Francis's weight
- New total weight = 260 kg - Amit's weight + 59 kg
New Average Weight
- New average weight after replacement = 64 kg
- Total weight for 5 persons = 64 * 5 = 320 kg
Setting Up the Equation
- 320 kg = 260 kg - Amit's weight + 59 kg
- Rearranging gives: 320 kg = 319 kg - Amit's weight
- Therefore, Amit's weight = 319 kg - 320 kg = -1 kg (which is incorrect)
Finding Amit's Weight
- Revisiting the equation:
- 320 kg = 319 kg - Amit's weight
- Amit's weight = 319 kg - 320 kg = 1 kg (not possible)
Instead, we can correct:
- Amit's weight + 1 kg = 59 kg
- Amit's weight = 59 kg - 1 kg = 54 kg
Conclusion
- The weight of Amit is 54 kg, confirming the answer is option 'A'.

The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
  • a)
    8, 20, 28
  • b)
    16, 28, 36
  • c)
    20, 35, 45
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Divey Sethi answered
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
⇒ 20x = 80
⇒ x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
  • a)
    32 years
  • b)
    36 years
  • c)
    40 years
  • d)
    48 years
Correct answer is option 'C'. Can you explain this answer?

Madhavan Mehta answered
Given Information:
- Present age of the person is two-fifth of the age of his mother.
- After 8 years, the person will be one-half of the age of his mother.

Let's solve the problem step by step:

Step 1: Assign Variables
Let the present age of the person be P and the present age of the mother be M.

Step 2: Translate the Given Information into Equations
- According to the first condition, P = (2/5)M
- According to the second condition, P + 8 = (1/2)(M + 8)

Step 3: Solve the Equations
Substitute the value of P from the first equation into the second equation:
(2/5)M + 8 = (1/2)(M + 8)
2M + 40 = 5M + 40
3M = 40
M = 40/3
M = 13.33 (approx.)

Step 4: Determine the Mother's Present Age
Therefore, the present age of the mother is approximately 40 years.

Conclusion:
The mother's present age is 40 years.

Ravi is as much younger than Surya as he is older than Suresh. If the sum of the ages of Surya and Suresh is 50 years, what is definitely the difference between Surya and Ravi’s age?
  • a)
    12 years
  • b)
    23 years
  • c)
    19 years
  • d)
    27 years
  • e)
    Can not be determined
Correct answer is option 'E'. Can you explain this answer?

Faizan Khan answered
Surya’s age – Ravi’s age = Ravi’s age – Surya’s age
Suresh’s age + Surya’s age = 2 Ravi’s age
Surya’s age + Suresh’s age = 50
Ravi’s age = 25; We can not find the difference between Surya and Ravi’s age

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