Math, asked by tiyathomas4446, 10 months ago

The ratio between the ages of a and b at present is 2:3 five years hence the ratio of their ages will be 3:4 what is the present age of a

Answers

Answered by sanketj
4

Let the present ages of A and B be x and y respectively.

According to first condⁿ

 \frac{x}{y}  =  \frac{2}{3}  \\ x =  \frac{2}{3} y \\ y =  \frac{3x}{2}

(always try to get denominators in factors of 2, 5 or 10)

Answered by Anonymous
12

Let present age of a be "2M" years and present age of b be "3M" years.

Five years hence,

  • Age of a = 2M + 5

  • Age of b = 3M + 5

》 Five years hence, ratio of their ages becomes 3:4.

According to question,

\rightarrow \:  \dfrac{2M \:  +  \: 5}{3M \:  +  \: 5}  \:  =  \:  \dfrac{3}{4}

Cross multiply them

\rightarrow \:  4(2M  \: +  \: 5) \:  =  \: 3(3M \:  +  \: 5)

\rightarrow \:  8M  \: +  \: 20\:  =  \: 9M \:  +  \: 15

\rightarrow \:  8M  \: -  \: 9M\:  =  \: 15 \:  -  \: 20

\rightarrow \: -  \: M\:  =  \:  -  \: 5

\rightarrow\boxed{  \: M\:  =  \: 5}

So,

Present age of a = 2(5)

\rightarrow{10} years

Present age of b = 3(5)

\rightarrow{15} years

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Present age of a = 10 years.

____________ [ ANSWER ]

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☆ VERIFICATION :

From above calculations we have M = 5

Put value of M in this :

\dfrac{2M \:  +  \: 5}{3M \:  +  \: 5}  \:  =  \:  \dfrac{3}{4}

=> \dfrac{2(5) \:  +  \: 5}{3(5) \:  +  \: 5}  \:  =  \:  \dfrac{3}{4}

=> \dfrac{10 \:  +  \: 5}{15 \:  +  \: 5}  \:  =  \:  \dfrac{3}{4}

=> \dfrac{15}{20}  \:  =  \:  \dfrac{3}{4}

=> \dfrac{3}{4}  \:  =  \:  \dfrac{3}{4}

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