Home
Class 14
MATHS
The respective ratio between Jia’s age 7...

The respective ratio between Jia’s age 7 years hence and her father’s age 4 years hence, will be `3 : 8`. The sum of Jia s age 3 years ago and her fathers age at that time was 38 years. What is Jia’s present age ?

A

16 years

B

8 years

C

12 years

D

13 years

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will define Jia's present age as \( x \) and her father's present age as \( y \). ### Step 1: Set up the first equation based on the ratio of their ages in the future. According to the problem, the ratio of Jia’s age 7 years hence to her father’s age 4 years hence is \( 3 : 8 \). Therefore, we can write the equation: \[ \frac{x + 7}{y + 4} = \frac{3}{8} \] ### Step 2: Cross-multiply to eliminate the fraction. Cross-multiplying gives us: \[ 8(x + 7) = 3(y + 4) \] ### Step 3: Expand both sides of the equation. Expanding both sides, we have: \[ 8x + 56 = 3y + 12 \] ### Step 4: Rearrange the equation to isolate \( y \). Rearranging gives us: \[ 8x - 3y = -44 \quad \text{(Equation 1)} \] ### Step 5: Set up the second equation based on the sum of their ages 3 years ago. The problem states that the sum of Jia's age 3 years ago and her father's age at that time was 38 years. Therefore, we can write the second equation as: \[ (x - 3) + (y - 3) = 38 \] ### Step 6: Simplify the second equation. Simplifying this gives: \[ x + y - 6 = 38 \] ### Step 7: Rearrange to isolate \( y \). Rearranging gives us: \[ x + y = 44 \quad \text{(Equation 2)} \] ### Step 8: Substitute Equation 2 into Equation 1. From Equation 2, we can express \( y \) in terms of \( x \): \[ y = 44 - x \] Substituting this into Equation 1 gives: \[ 8x - 3(44 - x) = -44 \] ### Step 9: Expand and simplify the equation. Expanding this gives: \[ 8x - 132 + 3x = -44 \] Combining like terms results in: \[ 11x - 132 = -44 \] ### Step 10: Solve for \( x \). Adding 132 to both sides gives: \[ 11x = 88 \] Dividing by 11 results in: \[ x = 8 \] ### Step 11: Find Jia’s present age. Thus, Jia's present age is: \[ \boxed{8} \text{ years} \]
Promotional Banner

Similar Questions

Explore conceptually related problems

Tom’s father is thrice as old as Tom. 10 years ago Tom’s father’s age was 7 times his age. What is Tom’s current age?

5 years ago, father's age was 8 times Rohan's age. 5 years hence, the ratio of father's age to Rohan's age will be 10:3 . What is Rohan's present age?

4 years hence the sum of ages of A and B will be 16 years more than the sum of the present ages of B and C. 4 years ago the sum of A’s age and C’s age was 32 years, then what is the present age of C?

The ratio of the present ages of a father and his son is 3 : 1 . The sum of their ages after five years is 58. Find the ratio of their ages 3 years ago.

4 years ago, the ratio of ½ of A’s age at that time and four times of B’s age at the time was 5:12. Eight years hence ½ of A’s age at that time will be less than B’s age at that time by 2 years. What is B’s present age a. 5 years b. 8 years c. 10 years d. 12 years e. 14 years

Eight year ago, Poorvi’s age was equal to the sum of the present ages of her one son and one daughter. Five years hence, the respective ratio between the ages of her daughter and her son that time will be 7:6. If Poorvi’s husbands is 7 years elder to her and his present age is three times the present age of their son, what is the present age of the daughter ? (in years) a. 13 years b. 19 years c. 23 years d. 15 years e. 27 years