Question

20. Ambrose is aged three times more than Andrew.
After 8 years, he would be two and a half times
of Andrew's age. After further 8 years, how many
times would Anil be of Andrew's age?​

Answer 1

Correct question

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Ambrose is aged three times more than Andrew. After 8 years, he would be two and a half times of Andrew's age. After further 8 years, how many times would Ambrose be of Andrew's age?

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$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• Ambrose is aged three times more than Andrew

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• After 8 years, he would be two and a half times of Andrew's age

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• After further 8 years, how many times would Ambrose be of Andrew's age

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Let Ambrose's present ae be x

• Let Andrew's present age be y

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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➠ x = 3y ------ (1)

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$\underline{\bold{\texttt{Ambrose's age after 8 years :}}}$

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➠ x + 8

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$\underline{\bold{\texttt{Andrew's age after 8 years :}}}$

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➠ y + 8

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Given that after 8 years, Ambrose would be two and a half times of Andrew's age

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➜ $\sf x + 8 = 2 \dfrac { 1 } { 2 } \times y + 8$

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➜ $\sf x + 8 = \dfrac { 5 } { 2 } \times y + 8$ ----- (2)

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⟮ Putting x = 3y from (1) to (2) ⟯

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➜ $\sf 3y + 8 = \dfrac { 5 } { 2 } \times y + 8$

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➜ $\sf (3y + 8) \times 2 = 5 \times y + 8$

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➜ 6y + 16 = 5y + 40

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➜ 6y - 5y = 40 - 16

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➨ y = 26 ----- (3)

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• Hence Andrew is 26 years old

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⟮ Putting y = 26 from (3) to (1) ⟯

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➜ x = 3y

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➜ x = 3(26)

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➨ x = 78

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• Hence Ambrose is 78 years old

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$\underline{\bold{\texttt{After further 8 years , Ambrose's age :}}}$

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➜ x + 8 + 8

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➜ x + 16

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➜ 78 + 16

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➨ 94

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• Hence after further 8 years Ambrose's age will be 94 years

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$\underline{\bold{\texttt{After further 8 years , Andrew's age :}}}$

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➜ y + 8 + 8

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➜ y + 16

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➜ 26 + 16

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➨ 42

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• Hence after further 8 years Andrew's age will be 42 years

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Now ratio of Ambrose's and Andrew's age after further 8 years

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➜ $\sf \dfrac { 94 } { 42 }$

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➜ $\sf \dfrac { 47 } { 21}$

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➨ $\sf 2 \dfrac { 5 } { 21 }$

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Hence after further 8 years, Ambrose will be $\sf 2 \dfrac { 5 } { 21 }$ times of Andrew's age

Answer 2

Answer:

After 16 years, Ambrose will be 8 more than two times the age of Andrew.

Step-by-step explanation:

Step 1:

Let Andrew's age be denoted by x.

Ambrose's age is three times more than Andrew's. Therefore, Ambrose's age will be 3x.

Step 2:

After 8 years, their ages will be (x + 8) and (3x + 8) respectively.

After 8 years, Ambrose's age will also be two and half times Andrew's age.

$3x+8=\frac{5}{2}(x+8)$

$2(3x+8)=5(x+8)$

$6x + 16=5x+40$

$6x-5x=40-16$

x = 24

3x = 72

Therefore, Andrew's current age is 24 years and Ambrose's current age is 72 years.

Step 3:

After 16 years, their ages will be

Andrew: 24 + 16 = 40 years

Ambrose: 72 + 16 = 88 years

Therefore, after 16 years, Ambrose will be 8 more than twice Andrew's age.

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