Question

anusha and ishi are in the ratio 4:5 if four year back there ages were in ratio 3:4 . Find there present age​

Answer 1

Answer:

The present ages are Anusha is 16 years and Ishi is 20 years.

Step-by-step explanation:

Given :

Present age Ratio = 4 : 5

Ratio of ages 4 years ago = 3 : 4

To find :

Their present ages

Solution :

Let the present ages be -

• Anusha as 4y
• Ishi as 5y

Ages 4 years ago -

• Anusha = (4y - 4)
• Ishi = (5y - 4)

$\boxed{\sf{ \frac{4y - 4}{5y - 4} = \frac{3}{4}}}$

$\sf{\implies} \: \dfrac{4y - 4}{5y - 4} = \dfrac{3}{4} \\ \\ \sf{\implies} \: 4(4y - 4) = 3(5y - 4) \\ \\ \sf{\implies} \: 16y - 16 = 15y - 12 \\ \\ \sf{\implies} \: 16y - 15y = - 12 + 16 \\ \\ \sf{\implies} \: y = 4$

★ Present ages -

Value of 4y

$\sf{\implies} \: 4(4) \\ \\ \sf{\implies} \: 16$

Anusha's present age = 16 years

$\rule{300}{1.5}$

Value of 5y

$\sf{\implies} \: 4(5) \\ \\ \sf{\implies} \: 20$

Ishi's present age = 20 years

$\therefore$Anusha is 16 year old and Ishi is 20 year old.

Answer 2

Question :--- Anusha and ishi are in the ratio 4:5 if four year back there ages were in ratio 3:4 . Find there present age ?

Solution :---

→ Let Present age of Anusha = 4x .

→ Present age of ishi = 5x .

So ,

→ 4 years before anusha was = (4x-4) years old.

→ 4 years before ishi was = (5x-4) years old.

Now, it is given that, 4 years before their ratio of ages were 3:4 .

So,

→ (4x-4) : (5x-4) = 3:4

or,

→ (4x-4) / (5x-4) = 3/4

Cross- Multiply we get,

→ 16x - 16 = 15x - 12

→ 16x - 15x = 16-12

→ x = 4

So,

→ Present age of Anusha = 4x = 4*4 = 16 years.

→ Present age of ishi = 5x = 5*4 = 20 years.

Hence, Anusha is 16 years old and ishi is 20 years old.

______________________________

Shortcut Trick to Solve Question :

⋆ Present Age⠀⠀➞ 4 Yrs.⠀⋆ Before Age

Anusha : ishi⠀⠀⠀⠀⠀⠀⠀⠀⠀Anusha : ishi

⠀ ⠀4 : 5⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀3 : 4

◗ Difference Between Ratios are Same, i.e. (5 - 4) = 1 and, (4 - 3) = 1

So,

Divide Year Gap By that Number.

↦ Year Gap / Difference of Age

↦ 4 Years / 1

↦ 4

Now, Just Multiply the Outcome (4 in this Case) with any of the Ratio of find Age.

Here we have to Find Present Age :---

◗ Anusha = (4 × 4) = 16 Years.

◗ ishi = (5 × 4) = 20 Years.

∴ Therefore, Present Age of Anusha is 16 Years and Present Age of ishi is 20 Years.