The sum of ages of A and B is 50 years. A said to B, “I am twice as old as you were when I was as old as you are. Find the present age of B.a)28b)20c)24d)12Correct answer is option 'B'. Can you explain this answer?

Question

The sum of ages of A and B is 50 years. A said to B, &#8220;I am twice as old as you were when I was as old as you are. Find the present age of B.a)28b)20c)24d)12Correct answer is option 'B'. Can you explain this answer?

Accepted Answer

Let the ages of A and B be a and b
Going by the statement step by step
A says “I am twice as old”=A says that age is twice some number which is a=2( _ )
"as you were" which talks about past, means B’s age some times ago...which is b-(how many years ago)
So, a=2(b- (how many years ago))
“when I was as old as you are" = when A was B’s age now= When A was b years old. So no. of years from now to back then will be A’s age now minus A’s age then =a-b
a=2(b-(a-b))
a=4b-2a
a=4b/3 …..1
Also a+b=49
a=49-b …..2
From 1 and 2
49-b=4b/3
4b/3+b=49
7b/3=49
b=49*3/7=21 years
a=28 years

Answer

A = 28, B = 21

let present age of A = x

a/q - present age of B = 49 - x ( since sum of their ages = 49)

difference between their ages = x - (49 -x) = 2x - 49 ----> (1)

when A's age was 49 - x

B's Age must be (A's age - their age difference)

B's past age = (49-x) - (2x - 49) = 98 - 3x

it is given that A' present age is twice the B's past age:

=> x = 2(98 - 3x)

7x = 196

value of x, A's current age = 28

Answer

Correct answer is 'B'

Answer

That is really too much confusing

Answer

Open Rd sharma chapter quadratic equation this question is the last question on age check there u get ur ans in steps

Answer

'if you give me 8 years of your age, then our ages will be in the ratio 3:1.' How old are A and B?

Let's assume that A's age is x years old and B's age is y years old.

According to the statement, the sum of their ages is 49 years: x + y = 49.

If B gives A 8 years of his age, B will be y - 8 years old and A will be x + 8 years old.

The ratio of their ages will be (x + 8)/(y - 8) = 3/1.

To solve this system of equations, we can eliminate x by multiplying both sides of the first equation by (x + 8):

(x + 8)(x + y) = 49(x + 8)

Expanding both sides:

x^2 + xy + 8x + 8y = 49x + 392

Rearranging the terms:

x^2 + xy - 41x + 8y - 392 = 0

Now, let's rearrange the second equation to get x in terms of y:

(x + 8)/(y - 8) = 3/1

Cross-multiplying:

x + 8 = 3y - 24

x = 3y - 32

Substituting this value of x into the first equation:

(3y - 32)^2 + (3y - 32)y - 41(3y - 32) + 8y - 392 = 0

Expanding and simplifying:

9y^2 - 96y + 1024 + 3y^2 - 96y + 992 - 123y + 1312 + 8y - 392 = 0

Combining like terms:

12y^2 - 307y + 2936 = 0

Now we can solve this quadratic equation using the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

y = (-(-307) ± √((-307)^2 - 4(12)(2936))) / (2(12))

Simplifying:

y = (307 ± √(94249 - 141408)) / 24

y = (307 ± √(-47159)) / 24

Since the square root of a negative number is not real, there are no real solutions for y. Therefore, there is no real solution for A and B's ages that satisfies the given conditions.

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