1. Four years ago, the ratio of the ages of A and B was 9 : 13. Eight years hence, the ratio of the ages of A and B will be 3 : 4. What will be the ratio of their ages 4 years hence?

चार वर्ष पहले, A और B की आयु का अनुपात 9 : 13 था। अब से आठ वर्ष के बाद, A और B की आयु का अनुपात 3 : 4 होगा। अब से 4 वर्ष के बाद उनकी आयु का अनुपात क्या होगा?

Option “A” is correct.

Given:

Four year ago the ratio of age of A and B is 9 : 13

Calculation:

⇒ (9x + 4 + 8)/(13x + 4 + 8) = 3/4

⇒ 36x + 48 = 39x + 36

⇒ x = 4

⇒ Present age of A = 9 × 4 + 4 = 40

⇒ Present age of B = 13 × 4 + 4 = 56

⇒ The ratio after 4 years = (40 + 4)/(56 + 4) = 44/60 = 11/15

∴ The required result will be 11/15.

2. The ratio of the present ages of Prabhu and Ramesh is 4 : 7, respectively. After 5 years, the ratio will change to 5 : 8. Find the present age of Prabhu.

प्रभु और रमेश की वर्तमान आयु का अनुपात क्रमशः 4 : 7 है। 5 वर्षों के बाद, अनुपात 5 : 8 में बदल जाएगा। प्रभु की वर्तमान आयु ज्ञात कीजिए।

Option “C” is correct.

Given:

The ratio of the present ages of Prabhu and Ramesh is 4 : 7

After 5 years, the ratio will change to 5 : 8.

Calculation:

The age of Prabhu is 4x

And age of Ramesh is 7x

According to the question

⇒ (4x + 5)/(7x + 5) = 5/8

⇒ 32x + 40 = 35x + 25

⇒ 3x = 15

⇒ x = 5

Age of Prabhu is 4x

⇒ 4 × 5 = 20 years

∴ The present age of Prabhu is 20 years.

3. 2 years ago, the average age of a family of 5 members was 18 years. After a new member is added to the family, the average age of the family is still the same. The present age of the newly added member, in years, is:

2 वर्ष पहले, 5 सदस्यों के एक परिवार की औसत आयु 18 वर्ष थी। परिवार में एक नया सदस्य जोड़ने के बाद, परिवार की औसत आयु अभी भी समान है। नए जोड़े गए सदस्य की वर्तमान आयु, वर्षों में है:

Option “A” is correct.

Given:

The average age of a family of 5 members 2 years ago was 18 years.

The average after a new member add to the family is 18 years.

Concept Used:

The average = Sum of the all numbers/Number of the numbers

Calculation:

The average age of a family of 5 members 2 years ago was 18 years.

The sum of age of all family member 2 years ago = 18 × 5 = 90

The sum of age of all family member at present = 90 + 2 × 5 = 100

Let the age of new member be x.

The sum of age of a family of 6 member = 6 × 18 = 108

⇒ 100 + x = 108

⇒ x = 8 years

∴ The age of new member of family is 8 years.

4. The present ages of A and B are in the ratio 3 : 4. Twelve years ago, their ages were in the ratio 2 : 3. The sum of the present ages of A and B (in years) is:

A और B की वर्तमान आयु 3 : 4 के अनुपात में है। बारह वर्ष पहले, उनकी आयु 2 : 3 के अनुपात में थी। A और B की वर्तमान आयु का योग (वर्षों में) क्या है?

Option “C” is correct.

Given:

Present age ratio of A and B = 3 : 4

Ratio of age of A and B before 12 years = 2 : 3

Calculation:

Let the present age of A and B be 3x and 4x

⇒ (3x – 12)/(4x – 12) = 2/3

⇒ 3× (3x – 12) = 2× (4x -12)

⇒ 9x – 36 = 8x – 24

⇒ 9x – 8x = 36 – 24

⇒ x = 12

The total present age is 4x + 3x

⇒ 7x =7 × 12 = 84

∴ The total present age is 84years.

5. The total of the ages of four persons is 86 years. What was their average age 4 years ago?

चार व्यक्तियों की कुल आयु का योग 86 वर्ष है। 4 साल पहले उनकी औसत आयु क्या थी?

Option “C” is correct.

Given:

The total age of four persons is 86 years

Formula Used:

The average age of persons = Sum of ages of Persons/number of persons

Calculation:

According to question,

We have to find the average age of persons 4 years ago

Sum of ages of person 4 years ago = 86 – 4 × 4

⇒ 86 – 16

⇒ 70

Now, Average age of four persons = 70/4

⇒ 17.5

Hence, the average age of four persons 4 years ago was 17.5

6. The ratio of present ages (in years) of a father and son is 15 : 8. Six years ago, the ratio of their ages was 13 : 6 What is the father’s present age ?

एक पिता और पुत्र की वर्तमान आयु (वर्षों में) का अनुपात 15 : 8 है। छह वर्ष पूर्व, उनकी आयु का अनुपात 13 : 6 था। पिता की वर्तमान आयु क्या है?

Option “B” is correct.

Given:

The ratio of present ages (in years) of a father and son is 15 : 8. Six years ago.

And the ratio of their ages was 13 : 6.

Calculation:

Let the present age of father be 15x years.

And the present age of son be 8x years.

According to the question:

(15x – 6)/(8x – 6 ) = 13/6

⇒ 90x – 36 = 104x – 78

⇒ – 14x = – 42

⇒ x = 3

∴  The present age of father is 15x years = 15 × 3 = 45 years.

7.The average ages of Kishore, his wife and their child 6 years ago was 38 years and that of his wife and their child 8 years ago was 32 years. Find the present age of Kishore.

किशोर, उसकी पत्नी और उसके बच्चे की औसत आयु 6 वर्ष पहले 38 वर्ष थी और उसकी पत्नी और उसके बच्चे की औसत आयु 8 वर्ष पहले 32 वर्ष थी। किशोर की वर्तमान आयु ज्ञात कीजिए।

Option “B” is correct.

Given:

The average age of Kishore, his wife, and their child 6 years ago was 38 years

The average age of Kishore’s wife and their child 8 years ago was 32 years

Concept used:

Average =Sum of total observations/Total number of observations

Calculation:

Sum of ages of all three members 6 years ago = 38 × 3

⇒  114 years

∴ Sum of ages of all three at present = 114 + (6 × 3)

⇒ 132 years

Also, from given data

Sum of ages of Kishore’s wife and child 8 years ago = 32 × 2

⇒  64 years

∴ Sum of ages of wife and the child at present = 64 + (8 × 2)

⇒ 80years

∴ The present age of Kishore is 132 – 80 i.e 52 years

8. The sum of the presents age of a father and son is 52 years Four years hence, the son’s age will be 1/4 that of the father. What will be the ratio of the age of the son and father, 10 years from now?

एक पिता और पुत्र की वर्तमान आयु का योग 52 वर्ष है। चार वर्ष बाद, पुत्र की आयु पिता की आयतु की 1/4 होगी। अब से 10 वर्ष बाद पुत्र और पिता की आयु का अनुपात क्या होगा?

Option “B” is correct.

Given:

Father’s present age + Son’s present age = 52 years

Son’s age after 4 years = 1/4 × Father’s age after 4 years

Concept used:

Using the concept of the linear equation.

Calculation:

Let the present age of the son be x years.

And the present age of the father is (52 – x) years.

According to the question,

Son’s age after 4 years = 1/4 × Father’s age after 4 years

⇒ (x + 4) = 1/4 × (52 – x + 4)

⇒ (x + 4) × 4 = 56 – x

⇒ 4x + 16 = 56 – x

⇒ 5x = 40

⇒ x = 8 years

Son’s present age = 8 years

Father’s present age = 52 – 8

⇒ Father’s present age = 44 years

Required ratio = (Age of son after 10 years)/(Age of father after 10 years)

⇒ Required ratio = (8 + 10)/(44 + 10)

⇒ Required ratio = 18/54

⇒ Required ratio = 1/3

∴ The ratio of the age of the son and father, 10 years from now is 1 ∶ 3.

9. The ratio of a man’s age to his father’s age is 4 : 5, and the ratio of his age to his son’s age is 6 : 1. Four years ago these ratios were 11 : 14 and 11 : 1, respectively. The ratio of the age of the grandfather to that of the grandson 12 years from now will be:

एक व्यक्ति और उसके पिता की आयु का अनुपात 4 : 5 है, और उसकी आयु और उसके पुत्र की आयु का अनुपात 6 : 1 है। चार वर्ष पहले ये अनुपात क्रमशः 11 : 14 और 11 : 1 थे। 12 वर्ष बाद दादा की आयु और पोते की आयु का अनुपात होगा:

Option “C” is correct.

Given:

The ratio of a man’s age to his father’s age = 4 : 5

The ratio of his age to his son’s age = 6 : 1

Four years ago age ratio of man to his father = 11 : 14

Four years ago age ratio of man to his son = 11 : 1

Calculation:

The ratio of a man’s age to his father’s age = 4 : 5

Four years ago age ratio of man to his father = 11 : 14

According to the question

(4x – 4)/(5x – 4) = 11/14

⇒ 14 (4x – 4) = 11 (5x – 4)

⇒ 56x – 56 = 55x – 44

⇒ 56x – 55x = 56 – 44

⇒ x = 12

Present age of man = 4 × 12 = 48 years

Present age of father = 5 × 12 = 60 years

The ratio of age of man to his son’s age = 6y : y

6y = 48

⇒ y = 8

Present age of son = 8 years

12 years after, age of father will be = 60 + 12 = 72 years

12 years after, age of his son = 8 + 12 = 20 years

∴ 12 years after age ratio of man’ father to that of his son = 72 : 20 = 18 : 5

10. A family consists of two grandparents, three parents and four grandchildren. The average age of the grand parents is 65 years, that of the parents is 32 years and that of the grand children is 8 years. What is the average age of the family?

एक परिवार में दादा-दादी, तीन अभिभावक और चार बच्चे शामिल हैं। दादा-दादी की औसत आयु 65 वर्ष है, अभिभावक की औसत आयु 32 वर्ष है और बच्चों की औसत आयु 8 वर्ष है। परिवार की औसत आयु क्या है?

Given :

Family has two grand parents, three parents and four children

Average age of grand parents is 65 years

Average age of parents is 32 years

Average age of grand children is 8 years

Calculations :

Total age of two grand parents = 65 × 2 = 130 years

Total age of three parents = 32 × 3 = 96 years

Total age of grand children = 8 × 4  = 32 years

Total family members = 2 + 3 + 4 = 9

Total age of family members = 130 + 96 + 32 = 258 years

Average age of the family = (total age/total number of persons)

⇒ 258/9

⇒ 28(2/3)

∴ The average age of family members = 28(2/3) years

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