Question

the age of A and B are in ratio 5:7 four year from now the ratio of their ages will be 3:4 Then the present age of B is​

Answer 1

Answer:

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Answer 2

AnswEr :

• Present Ratio of Age = 5 : 7
• Four Year From Now = 3 : 4
• Find Present Age of B.

Let the Present Age of A be 5n, and Present Age of B be 7n.

• According to the Question Now :

⇒ A + 4 years : B + 4 years = 3 : 4

⇒ (5n + 4) : (7n + 4) = 3 : 4

• Product of Mean = Product of Extreme

⇒ 4 × (5n + 4) = (7n + 4) × 3

⇒ 20n + 16 = 21n + 12

⇒ 16 - 12 = 21n - 20n

⇒ n = 4

_______________________________

• PRESENT AGES WILL BE :

◗ A = 5n = 5(4) = 20 Years

◗ B = 7n = 7(4) = 28 Years

∴ Hence, Present Age of B is 28 Years.

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• S H O R T C U T ⠀T R I C K :

⋆ Present Age⠀➞ 4 Yrs.⠀⋆ Future Age

⠀⠀A : B⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀A : B

⠀⠀5 : 7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 3 : 4

◗ Difference of both Ratios is

(7 - 5) = 2 and, (4 - 3) = 1, we will Multiply them by Opposite terms. Means by 1 in Present and By 2 in Future to make Difference Equal.

⠀⠀5 : 7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀3 : 4

× 1 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀× 2

_______________________________

⠀⠀5 : 7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀6 : 8

Now, Difference Between Ratios are Same, i.e. (7 - 5) = (8 - 6) = 2

So, we will find the Difference of Ratio in Ages, that Means we can find from any like A (6 - 5) = 1 or, B (8 - 7) = 1.

Divide Year Gap By that Number.

↦ Year Gap / Difference of Age

↦ 4 Years / 1

↦ 4

Now, Just Multiply the Outcome (4 in this Case) with any of the Ratio of find Age. Here we have to Find Present Age :

◗ A = (5 × 4) = 20 Years

◗ B = (7 × 4) = 28 Years

∴ Hence, Present Age of B is 28 Years.

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