Question

Dhruv and hemanthad 60 marbles altogether.After hemant gave 1/6 of his marbles to dhruv,dhruv had twice as many marbles as hemant. How many marbles had dhruv first?

Answer 1

Answer: Dhruv had 36 marbles.

Step-by-step explanation:

Let the Dhruv marble be D

Let the Hemant marble be  H

Total number of marbles = 60

∴ D + H = 60...(1)

Hemant gave 1/6 of his marble to Dhruv = 1/6× H =   H/6

Dhruv have marbles  , twice  marbles to Hemant

Now put in the equation

D + H/6 = 2 ( H × 5/6)

= 10 H /6

= 6 D = 9 H.... (2)

multiply with 6 equation 1

D + H =  60

6 D + 6 H = 60 ×6

(putting the 6D = 9H , Equation 2 )

9 H + 6H = 360

15 H = 360

H =  360 / 15

H = 24.

Hence, H = 24.

D = 6D = 9H

So, 6 D = 9 × 24

  6 D = 216

 D = 216 / 6

 D = 36.

Answer 2

solution:-

let,

x = Dhruv marbles

y = hemanth marbles

x+y = 60 ---------------(I)

x+y /6 = (2 y-y/6) -----------(II)

by using equation (II)

x+y/6 = 2(5y/6)

x+y/6 = 5y/3

multiply through by 6

6x + y = 10y

6x - 9y = 0

d + y= 60

6x - 9y = 0

We can solve by substitution or elimination.  Let's use elimination.

Multiply 1st by 9 and add equations.

9x+ 9y = 540

6x - 9y = 0

15 x = 540

x = 36 marbles originally


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@GauravSaxena01