Calculate Income Of the Month [Puzzle]

Question

Mr. Jill requires Rs 6000 per month to maintain his family. He saves 20% of any amount that he earns above Rs. 6000 but below Rs 7000 in a month. He saves 30% of amount that he earns above Rs 7000 but below Rs 8000 in a month. If Mr. Jill spends Rs 6975 on a month, what is his income for that month ?

Answer 1

Since you know the total amount spent in a month (6975), you could convert the saving percentages (20%, 30%) into spending percentages (80%, 70%).

So the total money spent are:

6000,                                   if income<6000
6000+0.8(income-6000)                   if income<7000
6000+0.8*1000+0.7(income-7000)          else

You have to check the money spent when income is 7000. This gives you 6800. Since he spent more than that, he earned more than 7000. So it's the third option ($income\ge7000$)

6000+800+0.7(income-7000)=6950

$0.7(income-7000)=150$

$income-7000=\frac{150}{0.7}$

$income=7000+\frac{150}{0.7}$