Question

*Sum of the present ages of Shruti and Kavita is 31. Shruti’s age 3 years ago was 4 times the age of Kavita. Find their present ages.*

1️⃣ Shruti 24, Kavita 7
2️⃣ Shruti 25, Kavita 6
3️⃣ Shruti 23, Kavita 8
4️⃣ Shruti 22, ​

Answer 1

Given:-

• Sum of present age of Shruti and Kavita = 31
• Three years ago Shruti's age is 4times the age of Kavita.

Find:-

• Present ages of Shruti and Kavita.

Solution:-

Let, The Present age of Shruti be 'x' yrs

and The Present age of Kavita be 'y' yrs

Now,

✬ Sum of Present age of Shruti and Kavita is 31.

➠ x + y = 31yrs.........〔Equation 1〕

Now,

✬ Three years ago:

→ Shruti's age = 'x - 3' yrs

→ Kavita's age 'y - 3' yrs

✬ Three years ago Shruti is four times tha age of Kavita.

↦x - 3 = 4(y - 3)

↦x - 3 = 4y - 12

↦x = 4y - 12 + 3

↦x = 4y - 9.........〔Equation 2〕

✦ Substituting the value of Equation 2 in Equation 1

→ x + y = 31

→ 4y - 9 + y = 31

→ 4y + y = 31 + 9

→ 5y = 40

→ y = 40/5 = 8yrs

→ y = 8yrs

✦ Now, Substituting value of y in Equation 2

↝x = 4y - 9

↝x = 4(8) - 9

↝x = 32 - 9

↝x = 23yrs

___________________________

Hence,

❍ Present Age of Shruti = 23yrs

❍ Present Age of Kavita = 8yrs

___________________________

So, Correct Option is 3️⃣ Shruti 23, Kavita 8