There were some apples and mangoes in Box U and Box V. In Box U, the ratio of the apples to the number of mangoes was 4 : 1. In Box V, the ratio of the number of apples to the number of mangoes was 3 : 2. There were 2 times as many fruits in Box U as in Box V. After another 20 mangoes were put into Box V, the ratio of the number of apples to the number of mangoes in Box V became 1 : 2. How many fruits were there in Box U?
Box U |
Box V |
2x5 = 10 u |
1x5 = 5 u |
Apples |
Mangoes |
Apples |
Mangoes |
4x2 |
1x2 |
3 |
2 |
8 u |
2 u |
3 u |
2 u |
The total number of fruits in Box U is repeated. Make the total number of fruits in Box U the same. LCM of 2 and 5 is 10.
The total number of fruits in Box V at first is repeated. Make the total number of fruits in Box V the same. LCM of 1 and 5 is 5.
|
Box U |
Box V |
|
Apples |
Mangoes |
Apples |
Mangoes |
Before |
8 u |
2 u |
3 u |
2 u |
Change |
|
|
|
+ 20 |
After
|
8 u
|
2 u
|
1x3 = 3 u |
2x3 = 6 u |
Number of apples in Box V remains unchanged. Make the number of apples in Box V the same. LCM of 3 and 1 is 3.
Number of mangoes put into Box V
= 6 u - 2 u
= 4 u
4 u = 20
1 u = 20 ÷ 4 = 5
Number of fruits in Box U
= 8 u + 2 u
= 10 u
= 10 x 5
= 50
Answer(s): 50