Question

the present age of two brothers are in the ratio 4: 3 four years leater their age will be in the ratio 6 : 5 what are the their present ages.​

Answer 1

★ Concept

This question (general age problem) is based on the concept of Ratio and Proportion. Given that the present ages of two brothers, say A and B are in the ratio of 4:3 i.e their current ages are 4x and 3x respectively. Now, Four years later it's obvious that the ages of both brothers will be 4 more than their current ages i.e (4x+4) and (3x+4) years respectively but according to the given question four yrs later their ages would be in the ratio of 6:5. Thus, we'll equate both possibilities of their ages and will get their present ages.

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Let's proceed with Calculation !!

Let the present ages of two Brothers (A & B) be 4x and 3x respectively.

➟Four years later

Age of A = (4x + 4) year

Age of B = (3x + 4) year

➟According to the question

$\sf \dfrac{A}{B} = \dfrac{6}{5}$

On equating both conditions, we get

$\sf \red{\dfrac{(4x + 4)}{(3x + 4)} } = \dfrac{6}{5}$

By Cross Multiplication, we get

$\sf \rightarrow5(4x + 4) = 6(3x + 4)$

$\rightarrow \sf\: 20x + 20 = 18x + 24$

$\rightarrow \sf \: 20x - 18x = 24 - 20$

$\to \sf 2x = 4 \\ \sf\ x = \cancel\dfrac{4}{2} \quad \therefore \underline{\boxed{ \sf\red{ x \: = 2}}}$

Now since we get the value of x, we can use this value for finding the current ages of both brothers (A & B)

Conclusion

Present age of A = 4x = 4×2 = 8 years

Present age of B = 3x = 3×2 = 6 years

✧The present ages of both brothers are 8 yrs and 6 yrs respectively.

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☞ Additional Information

Ratio compares quantities of the same kind in the same units.

You may also note that

1. In a ratio, order of terms is very important.
2. Ratio is a fraction, the ratio will remain unchanged if each term of the ratio is multiplied and divided by the same non zero number.
3. Ratio has no unit.

Answer 2

PROVIDED INFORMATION :-

• the present age of two brothers are in the ratio 4: 3

• four years leater their age will be in the ratio 6 : 5

TO FIND :-

• what are the their present ages = ?

UNDERSTANDING CONCEPT :-

Here the question is telling about ratio and proportion we have provided the present age of two brothers are in the ratio 4: 3 their age will be in the ratio 6 : 5 first we will cross multiply we get 2 then, we will multiply 4 with 2 and 3 with 2 we get the answer

information about Ratio and proportion:-

RATIO AND PROPORTION IS A PART OF THE MATHEMATICS.

RATIO AND PROPORTION MEANS THAT

THE NUMBER WHICH CAN BE DIVIDE

TO THE THAT TWO NUMBERS IS CALLED

THE RATIO AND PROPORTION

Ratio: -

A ratio is a comparison of two numbers.

We generally separate the two numbers in the

ratio with a colon ":". Suppose we want

to write the ratio of 8 and 12.We can write

this as 8:12 or as a fraction 8/12, and we say the ratio is eight to twelve.

Proportion:-

A proportion is an equation with a ratio

on each side. It is a statement that two ratios are equal.

3/4 = 6/8 is an example of a proportion.

When one of the four numbers in a proportion

is unknown, cross products

may be used to find

the unknown number. This is

called solving the proportion.

SOLUTION :-

Since the ratio of the present ages of

Ram and Rahim is given as 4:3, let the present ages of Ram be (4x) years and Rahim's be (3x) years.

Are four years,

first brother age = (4x + 4) year

second brother age = (3x + 4) years

According to the given condition,

(4x + 4) / (3x + 4) = 6/5

BY CROSSING MULTIPLICATION WE

GET :

5(4x + 4) = 6(3x + 4)

or 20 + 20 = 18x + 24

or 20x - 18x = 24 - 20

or 2x = 4

or X = 2

• Present age of first brother = (4 × 2) = 8years

• Present age of second brother =
• (3 x 2) = 6years

ADDITIONAL INFORMATION :-

WHAT IS DIRECT PROPORTION ?

The term direct proportion means

that two (or more) quantities increase or

decrease in the same ratio.

For example, in the purple paint

mixture, the ratio of blue to of 4:3. This does not necessarily mean we

every mixture would have 4 and 3 blue cans

WHAT IS INVERSE PROPORTION ?

INVERSE PROPORTION:

It is a relation between two quantities

such that one increases in proportion as

the other decreases