Question

16. Fill in the blanks:
(a) Ram is twice as old as Shyam. If 10 years ago, Ram was 4 times as old
as Shyam, then the present ages of Ram and Shyam are______,______
Give step by step explanation of your answer.​

Answer 1

Answer: Shyam is 18.

We have 4 variables: Sn, St, Rn, Rt

(Shyan now, Shyan Then, Ram now, Ram Then)

Rn = 24 (Ram is now 24)

Rn = 2 St (Ram now is 2 times the age of Shyan then)

Rt = Sn (Ram then is the same age as Shyan now)

Rn - Rt = Sn - St (The same time has passed since now and then)

Then it is all just algebra.

St = Sn - Rn + Rt

St = 2Rt - Rn

Rn = 2 (2Rt - Rn)

Rn = 4Rt - 2Rn

3Rn = 4Rt

Rt = 3/4 Rn

Rn =24

Rt = 18

Rt = Sn = 18

Check:

Rn - Rt = 24 - 18 = 6

Sn - St = 18 - 1/2 Rn = 18 -12 = 6

Hope this helps....

Answer 2

Given:

• Ram is twice as old as Shyam. If 10 years ago, Ram was 4 times as old.

To Find:

• their present ages

Solution:

↬ let ram's present age be x

↬and shyam's present age be y

so,$\tt{\blue{x = 2y}}$

10 years ago,

$\purple{➷}$ram's age equals x - 10

$\purple{➷}$Shyam's age equals y - 10

_____________________

★Let's frame up an equation;

➺x - 10 = 4(y-10)

➺x -10 = 4y - 40

➺x- 4y = -40+10

➺x- 4y = -30

_____________________

now let's put the value of 2y in the place of x

➺2y - 4y = - 30

➺- 2y = - 30

➺y = 15

_____________________

so, shyam age = 15(y)

ram's age = 30 (2y)

hope this helped.!

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