Rakesh had some apples and he divided them into two lots A and B. He sold the first lot at the rate ₹ 2 for 3apples and the second lot at rate of ₹ 1 per apple and got a total of ₹ 400. If he had sold the first lot at the rate of ₹ 1 per apple and the second lot at the rate of ₹4 for 5 apples, his total collection would have been ₹460 . Find the total number of apples he had.
Answers
Answer:
Let in lotA there are x apples
Let in lotB there are y apples
The above statement gives 2 equations
2/3*x+y=400
taking LCM in left side and solving the equation weget,
2x+3y=1200 - - - - - - - - - equation1
x+4/5*y=460
Similarly we can solve this equation also
We get
5x+4y=2300 - - - - - - - - - equation 2
Multiplying 5 in equation1,multiplying 2 in equation2 we get,
10x+15y=6000 - - - - equation3
(eq3-eq4) 10x+8y=4600 - - - - - equation4
(-) (-) (-)
___________
7y=1400
y=200
Sub y in equation1
2x+600=1200
2x=600
x=300
In lot A no. of apples=300
In lot B no. of apples =200
Step-by-step explanation:
Let the first lot =x and the second lot =y, both in Rs .
∴ total number of bananas =x+y
In the first case price of x bananas at the rate of Rs. 2 per 3 bananas =
3
2x
and price of y bananas at the rate of Rs. 1 per banana =y.
∴ by the given condition
3
2x
+y=400
⇒2x+3y=1200 ..............(i)
In the second case price of x bananas at the rate of Rs. 1 per banana =x and price of y bananas at the rate of Rs. 4 per 5 banana =
5
4
y
∴ by the given condition x+
5
4
y=460
⇒5x+4y=2300 ........(ii)
Multiplying (i) by 5 and (ii) by 2, we get
10x+15y=6000 ........(iii) and 10x+8y=4600 .........(iv)
Subtracting (iv) from (iii), we get
7y=1400
⇒y=200
Putting y=200 in (i), we get
2x+3×200=1200
⇒x=300
∴x+y=300+200=500
So, Vijay had 500 bananas.