High School

1. A bag contains [tex]112\frac{1}{2}[/tex] kg of rice. Two-fifths of it was eaten by rats. How much rice was eaten by the rats?

2. A man spends [tex]\frac{2}{5}[/tex] of his income and has ₹120 left. How much did he have initially?

Answer :

To solve the given problems, let's break them down step by step:

  1. Rice Eaten by Rats:

    The total amount of rice in the bag is [tex]112\frac{1}{2}[/tex] kg. To find out how much rice was eaten by rats, we need to calculate two-fifth ([tex]\frac{2}{5}[/tex]) of the total rice.

    First, convert the mixed fraction [tex]112\frac{1}{2}[/tex] into an improper fraction:

    [tex]112\frac{1}{2} = \frac{225}{2}[/tex]

    Now, calculate [tex]\frac{2}{5}[/tex] of [tex]\frac{225}{2}[/tex]:

    [tex]\frac{2}{5} \times \frac{225}{2} = \frac{2 \times 225}{5 \times 2} = \frac{450}{10} = 45\ ext{kg}[/tex]

    So, the amount of rice eaten by rats is 45 kg.

  2. Man's Initial Income:

    Let's denote the man's initial income as [tex]x[/tex]. According to the problem, he spends [tex]\frac{2}{5}[/tex] of his income and has ₹120 left.

    This means that after spending, he has [tex]\frac{3}{5}[/tex] of his income left (since [tex]1 - \frac{2}{5} = \frac{3}{5}[/tex]).

    Therefore, we can set up the equation:

    [tex]\frac{3}{5}x = 120[/tex]

    Solve for [tex]x[/tex] by multiplying both sides by 5:

    [tex]3x = 120 \times 5[/tex]

    [tex]3x = 600[/tex]

    Now, divide both sides by 3:

    [tex]x = \frac{600}{3} = 200[/tex]

    The man's initial income was ₹200.

In summary, 45 kg of rice was eaten by rats, and the man's initial income was ₹200.