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
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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
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Next →9
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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,
According to the question :
By doing cross multiplication we get :
Hence, the required ages of A and B are :
➲ Present age of A :
↦
↦
↦
➠
➲ Present age of B :
↦
↦
↦
➠
Hence, the correct options is option no (C) 72 years.
VERIFICATION :
By putting x = 9 we get,
Hence, Verified .
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 .