A fruit vendor bought some mangoes of which 10% were rotten. He sold 33 1/3% of the rest. Find the total number of mangoes bought by him initially, if he still has 240 mangoes with him.
original number --- x
number of good mangos = .9x
33 1/3% is exactly 1/3
so he still have 2/3 of the .9x mangoes left, that is
(2/3)(9/10)x = 240
(3/5)x = 240
x = 400
so he bought 400 mangoes.
check:
40 were rotten, so he had 360 to sell
he sold 1/3 or 120 of that, leaving him with 240
my answer is correct
Let the total no. of mangoes be x.
10% of the mangoes were rotten.
∴ remaining mangoes = x - 10x/100 = 90/100
The fruit vendor sold 33 1/3% of the remaining.
∴ mangoes still remaining with him
= 90x/100 - 3 * 100 * 90x
= 90x/100 - 90x/300
= (270x - 90x)/300
= 3x/5
By the problem,
3x/5 = 240
=> x = 80 * 5
=> x = 400
The fruit vendor bought 400 mangoes.
Let's go step-by-step to solve this problem.
Step 1: Calculate the number of mangoes after 10% were rotten:
Let x be the initial number of mangoes bought by the vendor.
After 10% were rotten, the vendor has (100% - 10% = 90%) of the mangoes remaining.
This can be represented as 90% of x, which is (90/100)x = 0.9x.
Step 2: Calculate the number of mangoes sold by the vendor:
The vendor sold 33 1/3% of the remaining mangoes.
This can be represented as (33 1/3/100) of 0.9x, which is (33 1/3/100) * 0.9x = (1/3 * 9/10 * x) = (3/10)x.
Step 3: Calculate the number of mangoes remaining with the vendor:
The vendor has 240 mangoes left, which is equal to (0.9x - (3/10)x) = (6/10)x.
So, (6/10)x = 240.
Step 4: Solve the equation to find x:
Multiply both sides of the equation by 10/6 to solve for x:
x = 240 * (10/6) = 400.
Therefore, the vendor initially bought 400 mangoes.
To solve this problem, we can follow these steps:
Step 1: Calculate the total number of rotten mangoes.
Let's assume the total number of mangoes bought by the vendor is "x". Since 10% of them were rotten, the number of rotten mangoes is (10/100) * x = x/10.
Step 2: Calculate the number of good mangoes.
The rest of the mangoes are the good ones, so the number of good mangoes is x - (x/10) = (9/10) * x.
Step 3: Calculate the number of mangoes sold.
The vendor sold 33 1/3% (or 1/3) of the good mangoes. So, the number of mangoes sold is (1/3) * (9/10) * x = (3/10) * x.
Step 4: Calculate the number of mangoes remaining.
The number of mangoes remaining is given as 240. So, we have (9/10) * x - (3/10) * x = 240.
Step 5: Solve the equation.
Combining like terms in Step 4, we get (6/10) * x = 240.
To isolate x, we divide both sides by (6/10):
x = (240 * 10) / 6 = 400.
Therefore, the initial total number of mangoes bought by the vendor is 400.