Question

12. Mrs Sharma is 27 years older than her caughter Neta After 8 years she will be twice as old as
Neha. Find their present ages.
13) Seema is 6 years older than her brother Vijay. If the sum of their ages is 28 years, what are
their present ages?
14. Roopak is twice as old as his brother Harsh. If the difference of their ages be 11 years, find
their present ages.
Equations​

Answer 1

Correct Questions:-

12) Mrs. Sharma is 27 years older than her daughter Neha. After 8 years she will be twice as old as Neha. Find their present ages.

13) Seema is 6 years older than her brother Vijay. If the sum of their ages is 28 years, what are their present ages?

14) Roopak is twice as old as his brother Harsh. Of the difference of their ages be 11 years, find their present ages.

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Required Solutions:-

12) Given:-

• Mrs.Sharma is 27 years older than her daughter Neha.
• After 8 years she will be twice as old as Neha.

To Find:-

• The present age of Neha and Mrs.Sharma

Solution:-

Let the age of Neha be x

Age of her mother = x + 27

After 7 years,

Age of Neha = (x + 8) years

Age of her mother = (x + 27 + 8) = (x + 35) years.

ATQ,

= x + 35 = 2(x + 8)

=> x + 35 = 2x + 16

=> x - 2x = 16 - 35

=> -x = -19

=> x = 19

Hence, the present ages of:-

Neha = x = 19 years

Mr.Sharma = x + 27 = 19 + 27 = 46 years.

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13) Given:-

• Seema is 6 years older than her brother Vijay.
• Sum of their ages is 28

To find:-

• Present ages of Vijay and Seema

Solution:-

Let the age of Vijay be x

Age of Seema = x + 6

ATQ,

(x) + (x + 6) = 28

=> x + x + 6 = 28

=> 2x = 28 - 6

=> 2x = 22

=> x = 22/2

=> x = 11

Hence, the present ages of:-

Vijay = x = 11 years

Seema = x + 6 = 17 years.

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14) Given:-

• Roopak is twice as old as his brother Harsh.
• Difference of their ages = 11 years.

To find:-

• Present age of Roopak and Harsh.

Solution:-

Let the present age of Harsh be x

Present age of Roopak = 2x

ATQ,

= 2x - x = 11

=> x = 11

Hence, the present ages of:-

Roopak = 2x = 2 × 11 = 22 years

Harsh = x = 11 years.

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Answer 2

Answer:

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12) Let Rekha's present age be x

Mrs. Goel's present age = x+27

After 8 years,

Age of Rekha=x+8

Age of Mrs. Goel =x+27+8

According to the question,

2(x+8)=x+27+8

2x+16=x+35

x=19

Therefore, Rekha's age=19 years

and Mrs. Goel=46 years.

13) Let Reena's present age be x years

⇒ Ajay's present age=x−6

and x+x−6=28

⇒ 2x=34

⇒ x=17

⇒ Reena's age=17,

Ajay's age=11.

14) let age of vikas be x

Given:

age of deepak = age of vikas +11

age of deepak =x+11

also age of deepak =2 (age of vikas)

age of deepak =2(x)....(2)

from (1) and (2)

x+11=2x

⇒ x=11

age of vikas =11 years, age of deepak =11+11=22 years