Question

A and B each has a certain number of mangoes A says to B ‘if you give 30 of your mangoes I will have twice as many as left with you’ B replies ‘if you give me 10 I will have thrice as left with you’. Then find how many mangoes each has.
A. A have 22 mangoes and B have 54 mangoes
B. A have 34 mangoes and B have 62 mangoes
C. A have 14 mangoes and B have 42 mangoes
D. A have 19 mangoes and B have 56 mangoes

Answer 1

Hint: We had to only assume the number of mangoes that A and B have and after that we can form two different equations from the given two cases. And on solving both equations we will get the number of mangoes that A and B have.

Complete step-by-step answer:
Let the number of mangoes A have is equal to x.
And the number of mangoes B have is equal to y.
So, we had to form two equations from the two given cases.
Case 1: When B gives 30 mangoes to A.
After getting 30 mangoes from B, A will have (x + 30) mangoes.
And the mangoes left with B will be (y – 30) mangoes.
Now A will have twice the number of mangoes left with B.
So, x + 30 = 2(y – 30)
Now solving the above equation. We get,
x + 30 = 2y – 60
x – 2y = – 60 – 30
x – 2y = – 90 (1)

Case 2: When A gives 10 mangoes to B.
After getting 10 mangoes from A, B will have (y + 10) mangoes.
And the mangoes left with A will be (x – 10) mangoes.
Now B will have thrice the number of mangoes left with A.
So, y + 10 = 3(x – 10)
Now solving the above equation. We get,
y + 10 = 3x – 30
y – 3x = – 30 – 10
y – 3x = – 40 (2)
Now we had to solve equation 1 and equation 2 to find the value of x and y.
So, for solving equation 1 and 2.
Multiplying equation 2 by 2. We get.
2y – 6x = – 80 (3)
Now adding equation 1 and equation 3. We get,
x – 6x = – 90 – 80 = – 170
– 5x = – 170
So, x = – 34
Now putting the value of x in equation 2. We get,
y – 3(34) = – 40
y – 102 = – 40
Adding both sides of the above equation by 102. We get,
y = 102 – 40 = 62
So, A have 34 mangoes and B have 62 mangoes.
Hence, the correct option will be B.

Note:- Whenever we come up with this type of problem then first, we have to form different equations from the different conditions. Now after that we had to solve the equations to find the value of x and y (number of mangoes A and B have). Now there is also an alternate method to solve the equations. We can solve one equation like we can find the value of x in terms of y from equation 1 and then we can put the value of x to equation 2. After that we will get the value of y. Now on putting the value of y in equation 1 we will get the required value of x.