Question

The ratio of present ages of Ramya and Saurabh is 8:7. After 10 years the ratio of their ages will be 12:11. What is Ramya's present age?

A) 20 B) 14 C) 63 D) 45

Answer 1

Answer:

A) 20

Present age of Ramya is 20 years.

Step-by-step explanation:

Given :

• The ratio of present ages of Ramya and Saurabh is 8:7

• After 10 years the ratio of their ages will be 12:11

Find:

• Ramya's present age

Solution:

Let,

Present age of Ramya = 8x

Present age of Saurabh = 7x

After 10 years:

Age of Ramya = 8x + 10

Age of Saurabh = 7x + 10

According to question :

⇒ $\frac{8x \: + \: 10}{7x \: + \: 10} \: = \frac{12}{11}$

⇒ 88x + 110 = 84x + 120

⇒ 88x - 84x = 120 - 110

⇒ 4x = 10

⇒ $x = \frac{10}{4}$

⇒ x = 2.5

So,

★ Present age of Ramya = 8x

⇒ 8(2.5)

⇒ 20

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \blue{Question:-}}}}}}$

The ratio of present ages of Ramya and Saurabh is 8:7. After 10 years the ratio of their ages will be 12:11. What is Ramya's present age?

A) 20 B) 14 C) 63 D) 45

_______________

${ \huge{ \bold{ \underline{ \underline{ \pink{Answer:-}}}}}}$

✒Given : -

• Ratio of Present ages of Ramya and Saurabh = 8:7
• After 10 years Ratio will be = 12:11

✒To Find : -

• Ramya's Present Age = ?

✒Let ,

• Present Age of Ramya = 8x
• Present Age of Saurabh = 7x

✒After 10 years : -

• Age of Ramya will be = 8x + 10
• Age of Saurabh will be = 7x + 10

$\leadsto\sf{{ \large{ \bold{ \underline{ \underline{ \purple{According\:to\:the\:Question:-}}}}}}}$

$\dashrightarrow\sf{\dfrac{8x+10}{7x+10}=\dfrac{12}{11}}$

$\dashrightarrow\sf{11x(8x+10)=12(7x+10)}$

$\dashrightarrow\sf{88x+110=84x+120}$

$\dashrightarrow\sf{4x=10}$

$\dashrightarrow\sf{x=\cancel\dfrac{10}{4}}$

$\leadsto\sf{{ \large{ \boxed{ \bold{ \bold{ \red{x=2.5}}}}}}}$

✒So ,

✒Now ,

$\dashrightarrow\sf{Present\:age\:of\:Ramya=8(x)}$

$\dashrightarrow\sf{8(2.5)}$

$\leadsto\sf{20\:years}$