Question

Ages of ravi and ram are in ratio 5 : 7.four years from now, the ratio of their ages will be 3 : 4. find what are the present ages of ravi and ram.

Answer 1

Solution

Given :-

• Ages of Ravi and Ram are in ratio 5 : 7
• four years from now, the ratio of their ages will be 3 : 4.

Find :-

• Present age of Ravi & Ram

Explanation

let,

• Present age of Ram = x years
• Present age of Ravi = y years

Case(1).

(Ages of Ravi and Ram are in ratio 5 : 7)

➡ x : y = 5:7

➡x/y = 5/7

➡7x - 5y = 0 ____________(1)

Case(2).

(four years from now, the ratio of their ages will be 3 : 4.)

➡ (x+4):(y+4) = 3:4

➡(x+4)/(y+4) = 3/4

➡4*(x+4) = 3*(y+4).

➡4x - 3y = 12 - 16

➡4x - 3y = -4 _____________(2)

Multiply by 3 in equ(1) & 5 in equ(2)

➡21x - 15y = 0 ____________(3)

➡20x - 15y = -20____________(4)

Sub. equ(3) & equ(4)

➡ 21x - 20x = 20

➡x = 20

Keep in equ(3)

➡ 21 × 20 - 15y = 0

➡15y = 21 × 20

➡y = 21 × 20/15

➡y = 21 × 4/3

➡y = 7 × 4

➡y = 21

Hence

• Present age of Ravi will be (x) = 20 years
• Present age of Ram will be (y) = 21 years

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