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:
500 Apples
Step-by-step explanation:
Let Say Lot A has A Apples
& Lot B has B Apples
Then,
Amount received = 2A/3 + B = 400
=> 2A + 3B = 1200 - eq 1
Selling lot,
A + 4B/5 = 460
=> 5A + 4B = 2300 - eq 2
3* eq2 - 4 * eq 1
=> 15A - 8A = 6900 - 4800
=> 7A = 2100
=> A = 300
2* 300 + 3B = 1200
=> B = 200
Total apples = 300 + 200 = 500
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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.