Raman Spends 2/5 of his monthly income on food and 3/8 of the remaining on clothes. Find the following:-
a. What fraction of his income is left with him?
b. If the money left is ₹2400, find his monthly income.
2/5 spent leaves 3/5
3/8 of 3/5 = 9/40
so, what's left is 1 - 2/5 - 9/40 = 3/8
So, 3/8 x = 2400
...
To find the fraction of Raman's income that is left with him, we need to subtract the fractions he spends on food and clothes from 1 (which represents the whole income).
a. Fraction of income left after spending on food = 1 - 2/5 = 3/5
This means 3/5 of Raman's income is still remaining after spending on food.
Now, let's calculate the fraction of the remaining income that is left after spending on clothes.
Fraction of remaining income left after spending on clothes = 3/5 - 3/8
To subtract fractions with different denominators, we need to find a common denominator. In this case, the least common multiple (LCM) of 5 and 8 is 40.
Converting the fractions to have a common denominator of 40:
(3/5) * (8/8) = 24/40
(3/8) * (5/5) = 15/40
So, the fraction of the remaining income left after spending on clothes is:
24/40 - 15/40 = 9/40
b. If the money left is ₹2400, we can set up a proportion to find Raman's monthly income:
Let's assume Raman's monthly income is x.
According to the given information,
9/40 * x = ₹2400
To solve for x (Raman's monthly income), we multiply both sides of the equation by 40/9:
x = ₹2400 * (40/9)
x = ₹10,666.67 (approx.)
Therefore, Raman's monthly income is approximately ₹10,666.67.