Question

Q-Five years ago,ram was three times as old as shyaam,four years from now,ram will be only twice as old as shyaam.what is the present age of ram
a-30
b-32
c-36
d-40

Answer 1

• Let present age of Ram be "M" years and present age of Shyam be "N" years.

Five years ago,

Age of Ram = (M - 5) years

Age of Shyam = (N - 5) years

》 Five years ago, Ram was three times as old as Shyam

According to question,

=> M - 5 = 3(N - 5)

=> M - 5 = 3N - 15

=> M = 3N - 15 + 5

=> M = 3N - 10 ________ (eq 1)

Fours years from now,

Age of Ram = (M + 4) years

Age of Shyam = (N + 4) years

》 Four years from now, Ram will be twice as old as Shyaam.

According to question,

=> (M + 4) = 2(N + 4)

=> M + 4 = 2N + 8

=> M = 2N + 4

=> 3N - 10 = 2N + 4 [From (eq 1)]

=> 3N - 2N = 4 + 10

=> N = 14

[ Present age of Shyaam ]

Put value of N in (eq 1)

=> M = 3(14) - 10

=> M = 42 - 10

=> M = 32

[ Present age of Ram ]

So,

Present age of Ram = 32 years

option b) 32

Answer 2

$\bf{\huge{\underline{\boxed{\rm{\red{Answer:}}}}}}$

Given :-

• Five years ago,Ram was three times as old as Shyaam
• Four years from now,Ram will be only twice as old as Shyaam

To find :-

• Present age of Ram

Solution :-

Let the present age of Ram be x years

Let the present age of Shyaam be y years

As per the first condition,

• Five years ago,Ram was three times as old as Shyaam

Five years ago,

Age of Ram = x - 5

Age of Shyaam = y - 5

Now let's form our first equation using the given condition,

x - 5 = 3 ( y - 5 )

x - 5 = 3y - 15

x - 3y = - 15 + 5

x - 3y = - 10 ------> 1

As per the second condition,

• Four years from now,Ram will be only twice as old as Shyaam.

Four years from now,

Age of Ram = x + 4

Age of Shyaam = y + 4

Let's form our second equation representing the condition mathematically,

x + 4 = 2 ( y + 4 )

x + 4 = 2y + 8

x - 2y = 8 - 4

x - 2y = 4 -----> 2

We have our two equations. Solve them via elimination method, simultaneously.

Subtract equation 2 from 1,

..+ x - 3y = - 10 -->1

( + x - 2y = + 4 )----> 2

__________________

- y = - 14

[Cancelling minus from both sides]

y = 14

Present age of Shyaam = y = 14 years

Substitute, y = 14, in equation 1,

x - 3y = - 10 -----> 1

x - 3 ( 14) = - 10

x - 42 = - 10

x = - 10 + 42

x = 32

Present age of Ram = x = 32 years

$\bf{\huge{\underline{\boxed{\tt{\pink{Verification:}}}}}}$

For first case :-

• Five years ago,Ram was three times as old as Shyaam

Five years ago,

Ram's age = 32 - 5 = 27

Shyaam's age = 14 - 5 = 9

Ram's was three times as old as Shyaam, so let's check if the condition satisfies.

27 = 3 (9)

27 = 27

LHS = RHS.

For second case :-

• Four years from now,Ram will be only twice as old as Shyaam

Four years from now,

Ram's age = 32 + 4 = 36 years

Shyaam's age = 14 + 4 = 18 years

Ram will be only twice as old as Shyaam, so let's check whether this condition is satisfied or not.

36 = 2 ( 18)

36 = 36

LHS = RHS.

Hence our answer is right.