Question

Question 11 of 32
Ratio of A and B is in the ratio 5: 8. After 6 years, the ratio of ages of A and B will be in the
ratio 17:26. Find the present age of B.
O A) 24
O B) 48
O C) 72
OD) 96
< Previous
Next →​9​

Answer 1

Answer:

Given :-

Ratio of A and B is in the ratio of 5 : 8. After 6 years, the ratio of ages of A and B will be in the ratio of 17 : 26.

To Find :-

What is the present age of B.

Solution :-

Let,

$\mapsto$ Present age of A be 5x years

$\mapsto$ Present age of B be 8x years

According to the question :

$\implies \sf \dfrac{5x + 6}{8x + 6} =\: \dfrac{17}{26}$

By doing cross multiplication we get :

$\implies \sf 17(8x + 6) =\: 26(5x + 6)$

$\implies \sf 136x + 102 =\: 130x + 156$

$\implies \sf 136x - 130x =\: 156 - 102$

$\implies \sf 6x =\: 54$

$\implies \sf x =\: \dfrac{\cancel{54}}{\cancel{6}}$

$\implies \sf\bold{\purple{x =\: 9\: years}}$

Hence, the required ages of A and B are :

➲ Present age of A :

↦ $\sf 5x\: years$

↦ $\sf 5(9)\: years$

↦ $\sf 5 \times 9\: years$

➠ $\sf\bold{\red{45\: years}}$

➲ Present age of B :

↦ $\sf 8x\: years$

↦ $\sf 8(9)\: years$

↦ $\sf 8 \times 9\: years$

➠ $\sf\bold{\red{72\: years}}$

$\therefore$ The present age of B is 72 years.

Hence, the correct options is option no (C) 72 years.

$\rule{300}{2}$

VERIFICATION :

$\mapsto \sf \dfrac{5x + 6}{8x + 6} =\: \dfrac{17}{26}$

By putting x = 9 we get,

$\mapsto \sf \dfrac{5(9) + 6}{8(9) + 6} =\: \dfrac{17}{26}$

$\mapsto \sf \dfrac{45 + 6}{72 + 6} =\: \dfrac{17}{26}$

$\mapsto \sf\dfrac{\cancel{51}}{\cancel{78}} =\: \dfrac{17}{26}$

$\mapsto \sf\bold{\green{\dfrac{17}{26} =\: \dfrac{17}{26}}}$

Hence, Verified .

Answer 2

Answer:

Answer:

Given :-

Ratio of A and B is in the ratio of 5 : 8. After 6 years, the ratio of ages of A and B will be in the ratio of 17 : 26.

To Find :-

What is the present age of B.

Solution :-

Let,

\mapsto↦ Present age of A be 5x years

\mapsto↦ Present age of B be 8x years

According to the question :

\implies \sf \dfrac{5x + 6}{8x + 6} =\: \dfrac{17}{26}⟹

8x+6

5x+6

=

26

17

By doing cross multiplication we get :

\implies \sf 17(8x + 6) =\: 26(5x + 6)⟹17(8x+6)=26(5x+6)

\implies \sf 136x + 102 =\: 130x + 156⟹136x+102=130x+156

\implies \sf 136x - 130x =\: 156 - 102⟹136x−130x=156−102

\implies \sf 6x =\: 54⟹6x=54

\implies \sf x =\: \dfrac{\cancel{54}}{\cancel{6}}⟹x=

6

54

\implies \sf\bold{\purple{x =\: 9\: years}}⟹x=9years

Hence, the required ages of A and B are :

➲ Present age of A :

↦ \sf 5x\: years5xyears

↦ \sf 5(9)\: years5(9)years

↦ \sf 5 \times 9\: years5×9years

➠ \sf\bold{\red{45\: years}}45years

➲ Present age of B :

↦ \sf 8x\: years8xyears

↦ \sf 8(9)\: years8(9)years

↦ \sf 8 \times 9\: years8×9years

➠ \sf\bold{\red{72\: years}}72years

\therefore∴ The present age of B is 72 years.

Hence, the correct options is option no (C) 72 years.

\rule{300}{2}

VERIFICATION :

\mapsto \sf \dfrac{5x + 6}{8x + 6} =\: \dfrac{17}{26}↦

8x+6

5x+6

=

26

17

By putting x = 9 we get,

\mapsto \sf \dfrac{5(9) + 6}{8(9) + 6} =\: \dfrac{17}{26}↦

8(9)+6

5(9)+6

=

26

17

\mapsto \sf \dfrac{45 + 6}{72 + 6} =\: \dfrac{17}{26}↦

72+6

45+6

=

26

17

\mapsto \sf\dfrac{\cancel{51}}{\cancel{78}} =\: \dfrac{17}{26}↦

78

51

=

26

17

\mapsto \sf\bold{\green{\dfrac{17}{26} =\: \dfrac{17}{26}}}↦

26

17

=

26

17

Hence, Verified .