Question

Mena and Mehul have some toffees. If Mona gives 30 toffees to Mehul, then Mehul will have twice
the toffees left with Mona. But if Mehul gives 10 toffees to Mona, then Mona will have thrice the
toffees as much as left with Mehul. How many toffees does each have?

Answer 1

Answer:

Mehul: 34 toffees

Mona : 62 toffees

Step-by-step explanation:

Let the toffees that Mona has be x and Mehul be y.

If Mona gives 30 toffees to Mehul then Mehul has = y + 30

This amount is twice what Mona has so we express this as :

x - 30 = (y + 30)/2

2x - 60 = y + 30

2x - y = 60 + 30

2x - y = 90…………………………i)

If Mehul gives Mona 10 toffees then Mona will have x + 10

This amount Mona has is twice as much as what Mehul is left with.

We write this below :

y - 10 = (x + 10)/3

3y - 30 = x + 10

3y - x = 10 + 30

3y - x = 40………………………ii)

We solve 1 and 2 simultaneously.

2x - y = 90

3y - x = 40

We multiply equation ii by 2 then add the two equations.

2x - y = 90

6y - 2x = 80

5y = 170

y = 170/5 = 34

We substitute this in equation 1 to get the value of x.

2x - 34 = 90

2x = 90 + 34

2x = 124

x = 124/2

x = 62

Mona had 62 toffees whereas Mehul had 34 toffees.