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
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Answer 1

Given :

• 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.

To Find :

• Present Age of B

Solution :

$\longmapsto\tt{Let\:Present\:age\:of\:A\:be=5x}$

$\longmapsto\tt{Let\:Present\:age\:of\:B\:be=8x}$

After 6 years :

$\longmapsto\tt{Age\:of\:A=5x+6}$

$\longmapsto\tt{Age\:of\:B=8x+6}$

A.T.Q :

$\longmapsto\tt{\dfrac{5x+6}{8x+6}=\dfrac{17}{26}}$

$\longmapsto\tt{26(5x+6)=17(8x+6)}$

$\longmapsto\tt{130x+156=136x+102}$

$\longmapsto\tt{130x-136x=102-156}$

$\longmapsto\tt{-6x=-54}$

$\longmapsto\tt{x=\cancel\dfrac{-54}{-6}}$

$\longmapsto\tt\bf{x=9}$

Value of x is 9 .

Therefore :

$\longmapsto\tt{Present\:Age\:of\:B=8(9)}$

$\longmapsto\tt\bf{72\:yrs}$

So , The Present Age of B is 72 yrs .

Option C)72 is Correct .

Answer 2

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 .