Question

4 year hence the ratio of ages a and b will be 5:7 and 6 year hence the ratio of ages will be 11:15 then find their present ages.​

Answer 1

Step-by-step explanation:

Let the age of A be 5x and age of B be 7x

After 6 years,

Age of A= 5x+6

Age of B = 7x+6

According to the question,

$(5x + 6):(7x + 6) = 11:15$

$\frac{5x + 6}{7x + 6} = \frac{11}{15}$

$15(5x + 6) = 11(7x + 6)$

$75x + 90 = 77x + 66$

$75x - 77x = 66 - 90$

$- 2x = - 26$

$x = \frac{ - 26}{ - 2}$

$x = 13$

Therefore,

Age of A= 5×13

= 65

Age of B = 7×13

=91

Answer 2

GIVEN :-

• 4 years hence , the ratio of ages of a and b will be 5:7.
• 6 years hence , the ratio of ages will be 11:15.

TO FIND :-

• Present ages of a and b.

SOLUTION :-

Let present age of a be 'x' yrs and b be 'y' yrs.

♦ 4 years hence,

• Age of a → (x + 4) yrs
• Age of b → (y + 4) yrs

And the ratio is 5:7.

$\\ \sf \: \dfrac{x + 4}{y + 4} = \dfrac{5}{7}$

Cross multiplying ,

$\\ \implies\sf \: 7(x + 4) = 5(y + 4) \\ \\ \implies \sf \: 7x + 28 = 5y + 20 \\ \\ \implies \sf \: 7x - 5y = 20 - 28 \\ \\ \implies\sf \: 7x - 5y = - 8 \\ \\ \sf \: multiplying \: whole \: equation \: by \: 22 \\ \\ \implies \underline{\sf \: 154x - 110y = - 176} \: \: \: \: \: \: - - (1)$

Also ,

♦ 6 years hence,

• Age of a → (x + 6) yrs
• Age of b → (y + 6) yrs

And ratio is 11:15.

$\\ \sf \: \dfrac{x + 6}{y + 6} = \dfrac{11}{15}$

Cross multiplying,

$\\ \implies \sf \: 15(x + 6) = 11(y + 6) \\ \\ \implies \sf \: 15x + 90 = 11y + 66 \\ \\ \implies \sf \: 15x - 11y = 66 - 90 \\ \\ \implies \sf \: 15x - 11y = - 24 \\ \\ \sf \: multiplying \: whole \: equation \: by \: 10 \\ \\ \implies \underline{\sf\: 150x - 110y = - 240}\: \: \: \: \: - - (2)$

Now , subtracting equation (2) by equation (1) ,

→ 154x - 110y - (150x - 110y) = -176 - (-240)

→ 154x - 110y - 150x + 110y = -176 + 240

→ 4x = 64

→ x = 64/4

→ x = 16

Now , substituting value of x in equation (2) ,

→ 150(16) - 110y = -240

→ 2400 - 110y = -240

→ -110y = -240 - 2400

→ -110y = -2640

→ y = -2640/-110

→ y = 24

Hence , age of a is 16years and age of b is 24years.