A man spend 1/3 of his income on food, of the rest 1/4 on bills and 1/5 on miscellaneous things. Finally he left with Rs.1760. Find his income?
a)4200 b)4600 c)4800) d)5200
To solve this problem, we can work backwards by reverse calculating the income.
Let's start by calculating the amount left after spending on miscellaneous things. We know that 1/5 of the remaining income is equal to Rs. 1760. So, we can set up the following equation:
(1/5) * Remaining income = Rs. 1760
To find the remaining income, we can multiply both sides of the equation by 5:
Remaining income = Rs. 1760 * 5
Remaining income = Rs. 8800
Now, let's calculate the bills. We know that 1/4 of the remaining income is spent on bills. So, we can set up the following equation:
(1/4) * Remaining income = Bills
Substituting the value of the remaining income we calculated earlier:
(1/4) * Rs. 8800 = Bills
To find the bills, we multiply:
Bills = Rs. 8800 * (1/4)
Bills = Rs. 2200
Next, let's calculate the amount spent on food. We know that 1/3 of the total income is spent on food. So, we can set up the following equation:
(1/3) * Total income = Food expenses
Substituting the value of the total income we want to find:
(1/3) * Total income = Rs. 2200
To find the total income, we multiply both sides by 3:
Total income = Rs. 2200 * 3
Total income = Rs. 6600
Therefore, the answer is Rs. 6600, which is not among the given options. It seems there might be an error in the options provided, as none of them match the calculated income.
Let's break down the problem step by step:
Step 1: Let's assume the man's income is represented by 'X'.
Step 2: The man spends 1/3 of his income on food, which means he has (2/3)X remaining.
Step 3: Out of the remaining income, the man spends 1/4 on bills. This leaves him with (3/4) * (2/3)X = (1/2)X.
Step 4: Out of this remaining income, the man spends 1/5 on miscellaneous things. This leaves him with (4/5) * (1/2)X = (2/5)X.
Step 5: Finally, the man is left with Rs. 1760, so we can set up the equation: (2/5)X = 1760.
To find X, we can solve this equation:
(2/5)X = 1760
X = (1760 * 5) / 2
X = 4400.
Therefore, the man's income is Rs. 4400.
Checking the options, we can see that the closest value is option a) 4200. However, since none of the given options match exactly, it is possible that there is a mistake in the question or the answer choices.
let his income be x
after food expenses he is left with (2/3)x
he then spends (1/4+1/5)(2x/3) = (3/10)x
which leaves him with 2x/3 - 3x/10 or 11x/30
(11/30)x = 1760
x = 4800 which is choice c)