A and b have some apples divided among themselves. a says to b if i give you 25% of the apples i have, i will still have 2 more apples than you. to this, b says if you give me apples equal to 70% of what i have now, i will have 4 more apples than you. what is the average number of apples that they have
Answers
The average number of apples that they have is 32
Given :
- A and B have some apples divided among themselves.
- A says to B if I give you 25% of the apples I have, I will still have 2 more apples than you.
- To this, B says if you give me apples equal to 70% of what I have now, I will have 4 more apples than you.
To find :
The average number of apples that they have
Solution :
Step 1 of 3 :
Form system of equations to calculate number of apples that they have
Let A have 100x apples and B have 100y apples
Now A says to B if I give you 25% of the apples I have, I will still have 2 more apples than you
100x - 25x = 100y + 25x + 2
⇒ 50x - 100y = 2 - - - - - (1)
Again B says if you give me apples equal to 70% of what I have now, I will have 4 more apples than you.
100x - 70y = 100y + 70y - 4
⇒ 100x - 240y = - 4 - - - - - (2)
Step 2 of 3 :
Calculate number of apples that they have
50x - 100y = 2 - - - - - (1)
100x - 240y = - 4 - - - - - (2)
Multiplying both sides of Equation 1 by 2 we get
100x - 200y = 4 - - - - - (3)
Equation 2 - Equation 3 gives
- 40y = - 8
⇒ y = 0.2
From Equation 1 we get
50x - (100 × 0.2) = 2
⇒ 50x - 20 = 2
⇒ 50x = 22
⇒ x = 0.44
So A have 44 apples and B have 20 apples
Step 3 of 3 :
Calculate average number of apples that they have
A have 44 apples and B have 20 apples
Total number of apples that they have
= 44 + 20
= 64
Number of persons = 2
Hence average number of apples that they have
= 64/2
= 32
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