Question

ration (08)
1) The ages of A and B are in ratio 5:7. Four years from now ratio of their ages will be 3:4,the
present age of B is:
(a) 15 years
(b) 20 years
(c) 28 years
(d) none of these​

Answer 1

➤ Correct Question:

The ages of A and B are in ratio 5:7. Four years from now ratio of their ages will be 3:4, the  present age of B is:

a. 15 years

b. 20 years

c. 28 years

d. None of these

➤ Given:

Present ages of A and B in

• Ratio = 5:7

Age of A and B after 4 years in

• Ratio = 3:4

➤ What To Find:

We have to find

• The present age of B

➤ Solution:

Let us take x as the common measure in ratio 5:7.

$\sf \Longrightarrow 5x \: and \: 7x$

Therefore, the equation will be,

$\sf \Longrightarrow \dfrac{5x + 4 }{7x + 4} = \dfrac{3}{4}$

Using cross multiplication,

$\sf \Longrightarrow (5x + 4 )\times 4 = 3 \times (7x + 4)$

Multiply 5x + 4by 4,

$\sf \Longrightarrow 20x + 16 = 3 \times (7x + 4)$

Multiply 7x + 4 by 3,

$\sf \Longrightarrow 20x + 16 = 21x + 12$

Take 20x to RHS,

$\sf \Longrightarrow 16 = 21x + 12 - 20x$

Take 12 to LHS,

$\sf \Longrightarrow 16 - 12= 21x - 20x$

Subtract 12 from 16,

$\sf \Longrightarrow 4 = 21x - 20x$

Subtract 21x to 20x,

$\sf \Longrightarrow 4 = x$

Now, substitute the values,

$\sf \Longrightarrow Present \: age \: of \: A = 5 \times 4 = 20 \: years$

$\sf \Longrightarrow Present \: age \: of \: B = 7 \times 4 = 28 \: years$

∴ Therefore, the present age of B is 28 years i.e option c.

Answer 2

QuestioN :

1) The ages of A and B are in ratio 5:7. Four years from now ratio of their ages will be 3:4,the  present age of B is:

(a) 15 years

(b) 20 years

(c) 28 years

(d) none of these​

GiveN :

• 15 years
• 20 years
• 28 years
• none of these​

To FiNd :

• The present age of B.

ANswer :

The present age of B is 28 years.

SolutioN :

Let present age of a be x years and b be years.

$\sf \frac{x}{y} =\frac{5}{7}$

$\sf 7x -5y=0$    ---[ 1 ]

$\sf \frac{x+4}{y+4} = \frac{3}{4}$

$\sf 4x+16=3y+12$

$\sf 4x-3y= -4$   ---[ 2 ]

Multiplying 1 with -3

$\sf -21x+15y=0$  ---[ 3 ]

Multiplying 2 with 5

$\sf 20x-15y=-20$ ---[ 4 ]

Adding 3 and 4

$\sf -x=-20$

$\sf = 20$

put x = 20 in 1

$\sf 7\:x\:20- 5y=0$

$\sf -5y=-140$

$\sf y = \frac{-140}{-5}$

$\sf y =28$

∴Hence, The present age of B is 28 years.

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