Question

A is 15 years older than b. Ten years,ago a was four time b's age what are their ages now?

Answer 1

GIVEN

A is 15 yrs older than B

A = B + 15 ...eq.01

Now, according to the Question

A - 10 = 4(B - 10)

=> A - 10 = 4(B - 10)

=> A - 10 = 4B - 40

=> A = 4B - 30

=> A = 4B - 30 ...eq.02

Now equation eq.01 and 02 ,

B + 15 = 4B - 30

=> - 3B = -45

=> B = 15

Now , A = 15 + 15 = 30

Hence age of A is 30yrs and B is 15yrs.

Answer 2

$\large{\underline{\underline{\mathfrak{\bf{QUESTION:-}}}}}$

• A is 15 years older than b. Ten years,ago a was four time b's age what are their ages now ?

$\large{\underline{\underline{\mathfrak{\bf{SOLUTION:-}}}}}$

$\bold{\red{\underline{\:GIVEN\:HERE:-}}}$

• A is 15 years older than b.
• Ten years,ago A was four time B's age .

$\bold{\red{\underline{\:FIND\:HERE:-}}}$

• Ages of A and B .

$\large{\underline{\underline{\mathfrak{\bf{\:EXPLANATION:-}}}}}$

Let,

• Age of A = x
• Age of B =y

A/C to question

$\hookrightarrow\:x\:=\:y+15$

$\hookrightarrow\:x\:-\:y\:=\:15$....(1)

And,

$\hookrightarrow\:(x-10)\:=\:4(y-10)$

$\hookrightarrow\:(x-4y)\:=\:-30$...(2)

Subtract equation (1) - (2)

$\hookrightarrow\:(3y)\:=\:15$

$\hookrightarrow\:y\:=\cancel{\frac{15}{3}}$

$\hookrightarrow\bold{\boxed{\boxed{\:y\:=\:5}}}$

Keep value of y in (1)

$\hookrightarrow\:(x-15)\:=\:15$

$\hookrightarrow\:x\:=\:(15+15)$

$\hookrightarrow\bold{\boxed{\boxed{\:x\:=\:30}}}$

____________________

$\red{\underbrace{Answer}}$

• Age of A = 30 years
• Age of B = 15 years

_____________________