Lydia spent 4/5 of her money on a mobile phone and 2/3 of the remaining amount on a bag. She had $60 left. How much more money did she spend on the mobile phone than on the bag?

Sure, let's solve this step by step:

1. First, let's find out how much money Lydia had left after buying the mobile phone. If she spent 4/5 of her money on the phone, then she had 1/5 of her money left. We know that this amount is equal to the money she spent on the bag plus the $60 she had left. Let's denote the total amount of money Lydia had as X. So, we have the equation: 1/5*X = money spent on bag +$60.

2. Next, we know that Lydia spent 2/3 of the remaining money on the bag. So, the money spent on the bag is 2/3*(1/5X) = 2/15X.

3. We can now substitute the money spent on the bag from the second step into the first equation: 1/5X = 2/15X + $60.

4. To solve for X, we can first multiply every term by 15 to get rid of the fractions: 3X = 2X + $900.

5. Subtract 2*X from both sides to get: X = $900.

6. Now that we know the total amount of money Lydia had, we can find out how much she spent on the mobile phone and the bag. She spent 4/5*$900 =$720 on the mobile phone and 2/15*$900 =$120 on the bag.

7. Finally, to find out how much more she spent on the mobile phone than on the bag, subtract the cost of the bag from the cost of the mobile phone: $720 -$120 = $600.

So, Lydia spent $600 more on the mobile phone than on the bag.