Question

£50 is divided between Alex, Peter & Angad so that Alex gets twice as much as Peter, and Peter gets three times as much as Angad. How much does Alex get?

Answer 1

The amount of money received by Ales is, £30.

Step-by-step explanation:

The total amount of money is £50.

Let X₁ = amount of money Alex gets, X₂ = amount of money Peter gets and X₃ = amount of money Angad gets.

It is provided that:

X₁ = 2X₂

X₂ = 3X₃

⇒ X₁ = 2 × 3X₃ = 6X₃

Then the equation representing the total amount is:

6X₃ + 3X₃ + X₃ = 50

                10X₃ = 50

                     X₃ = £5

Then the amount received by Peter is,

X₂ = 3X₃ = 3 × 5 = £15

Amount received by Alex is,

X₁ = 6X₃ = 6 × 5 = £30

Thus, the amount of money received by Ales is, £30.

Answer 2

Given :

Total money that is been divided between Alex, Peter and Angad = $\pounds$50

Amount received by Alex =  twice as much as received by Peter

Amount received by Peter = three times as much as Amount received by Angad

To Find :

The Amount received by Alex

Solution :

Let The Amount received by Alex = $\pounds$x

Let The Amount received by Peter = $\pounds$y

Let The Amount received by Angad = $\pounds$z

According to question

∵  Total money that is been divided = $\pounds$50

i.e       x + y + z = 50               .........1

∵  Amount received by Alex = 2 ×  Amount received by Peter

So,           x = 2 y             .............2

Amount received by Peter = 3 × Amount received by Angad

So,           y = 3 z           ............3

Solving eq 1 , 2 and 3

     x +  $\dfrac{x}{2}$  +  $\dfrac{y}{3}$  = 50  

or,  x + $\dfrac{x}{2}$  +  $\dfrac{x}{6}$  = 50

Taking L C M

       $\dfrac{6 x+ 3 x + x}{6}$   = 50

Or,   6 x + 3 x + x = 50 × 6

Or,                   10 x = 300

∴                          x = $\dfrac{300}{10}$

i.e                         x = $\pounds$30

So,  The Amount received by Alex =  x = $\pounds$ 30

The Amount received by Peter = y =  $\pounds$ $\dfrac{x}{2}$  = $\pounds$ 15

Let The Amount received by Angad = z = $\dfrac{y}{3}$  = $\pounds$ 5

Hence The Amount received by Alex  is  $\pounds$ 30  . Answer