Question

the age of a and b are in the ratio 5 is to 3 after 6 years there age will be in the ratio 7 is to 5 the present age A is​

Answer 1

• Let present age of a be 5M and present age of b be 3M.

» After six years.

Age of a = 5M + 6

And age of n = 3M + 6

• And the ratio of their ages is 7:5

A.T.Q.

=> $\dfrac{5M\:+\:6}{3M\:+\:6}$ = $\dfrac{7}{5}$

Cross-multiply them

=> 5(5M + 6) = 7(3M + 6)

=> 25M + 30 = 21M + 18

=> 25M - 21M = 18 - 30

=> - 4 M = - 12

=> M = 3

_______________________________

Present age of a = 5M = 5 × 3 = 15 years.

Present age of b = 3M = 3 × 3 = 9 years

____________ [ANSWER]

✡ $\dfrac{5M\:+\:6}{3M\:+\:6}$ = $\dfrac{7}{5}$

Put value of M in above equation.

=> $\dfrac{5(3)\:+\:6}{3(3)\:+\:6}$ = $\dfrac{7}{5}$

=> $\dfrac{15\:+\:6}{9\:+\:6}$ = $\dfrac{7}{5}$

=> $\dfrac{21}{15}$ = $\dfrac{7}{5}$

=> $\dfrac{7}{5}$ = $\dfrac{7}{5}$

___________ [HENCE VERIFIED]

Answer 2

➬ Present age of A = 15 Years

Step-by-step explanation:

Given:

• Age of a and b are in ratio 5:3.
• After 5 years their ages will be in ratio 7:5.

To Find:

• What is the present age of a ?

Solution: Let x be the common in given ratio.

• A's age = 5x
• B's age = 3x

• After 6 years their ages will be •

• A's age = (5x + 6) Years
• B's age = (3x + 6) Years

Now, a/q

$\implies{\rm }$ (5x + 6)/(3x + 6) = 7/5

$\implies{\rm }$ 5(5x + 6) = 7(3x + 6) [ By cross multiplication ]

$\implies{\rm }$ 25x + 30 = 21x + 42

$\implies{\rm }$ 25x – 21x = 42 – 30

$\implies{\rm }$ 4x = 12

$\implies{\rm }$ x = 12/4

$\implies{\rm }$ x = 3 Years

Hence, Present age of A = 5x = 5(3) = 15 Years

Present age of B = 3x = 3(3) = 9 Years

____________________

★ ChEck ★

➽ (5x + 6)/(3x + 6) = 7/5

➽ (15 + 6)/(9 + 6) = 7/5

➽ 21/15 = 7/5

➽ 7/5 = 7/5 { LHS = RHS }