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Q.

The ratio of the present ages of two brothers is 4:5. After 10 years, the ratio of their ages would be 6:7. Find the age of the elder brother after 15 years.

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a

35 years

b

40 years

c

50 years

d

25 years

answer is B.

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Detailed Solution

Concept- Assume that one brother is "x" years old and the other is "y" years old. In accordance with the requirements, create two linear equations in two variables and resolve for x and y. To find the solution, multiply the younger brother's age by 15, who is discovered to be older.
Let's suppose that one brother is

"x"

years old and the other is

"y"

years old. Given that they are currently four to five years apart in age, In light of this, mathematically

x : y = 4 : 5

Changing this into fraction, we get,

\frac{x}{y}

=

\frac{4}{5}

x = \frac{4 y}{5} . .

......................(i)
The first brother will be (x+10) years old after 10 years, while the second brother will be (y+10) years old. It is assumed that their ages will be 6:7 after 10 years. In light of this, mathematically

(x + 10) : (y + 10) = 6 : 7

Changing this into fraction, we get,

\frac{x + 10}{y + 10}

=

\frac{6}{7}

By cross-multiplication we have,

7 x + 70 = 6 y + 60

6y−7x=10...................(ii)
When the value of x from equation I is substituted in equation (ii) , we obtain

6 y - 7 \times \frac{4 y}{5} = 10

6 y - \frac{28 y}{5} = 10

\frac{30 y - 28 y}{5} = 10

\frac{2 y}{5} = 10

2 y = 50

y = 25

Now, substituting the value of y in equation (i) , we get,

x = 4 \times \frac{25}{5}

x = 20

The older brother is now 25 years old. His age will therefore be

: 25 + 15 = 40

years after 15 years.
Hence, the correct option is

2

.
ExamType: CBSE

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