There were some pomegranates and mangoes in Box J and Box K. In Box J, the ratio of the pomegranates to the number of mangoes was 3 : 1. In Box K, the ratio of the number of pomegranates to the number of mangoes was 3 : 1. There were 2 times as many fruits in Box J as in Box K. After another 99 mangoes were put into Box K, the ratio of the number of pomegranates to the number of mangoes in Box K became 1 : 4. How many fruits were there in Box K in the end?
| Box J |
Box K |
2x4 =
8 u |
1x4 =
4 u |
| Pomegranates |
Mangoes |
Pomegranates |
Mangoes |
| 3x2 |
1x2 |
3 |
1 |
| 6 u |
2 u |
3 u |
1 u |
The total number of fruits in Box J is repeated. Make the total number of fruits in Box J the same. LCM of 2 and 4 is 8.
The total number of fruits in Box K at first is repeated. Make the total number of fruits in Box K the same. LCM of 1 and 4 is 4.
| |
Box J |
Box K |
| |
Pomegranates |
Mangoes |
Pomegranates |
Mangoes |
| Before |
6 u |
2 u |
3 u |
1 u |
| Change |
|
|
|
+ 99 |
After
|
6 u
|
2 u
|
1x3 =
3 u |
4x3 =
12 u |
Number of pomegranates in Box K remains unchanged. Make the number of pomegranates in Box K the same. LCM of 3 and 1 is 3.
Number of mangoes put into Box K
= 12 u - 1 u
= 11 u
11 u = 99
1 u = 99 ÷ 11 = 9
Number of fruits in Box K in the end
= 3 u + 12 u
= 15 u
= 15 x 9
= 135
Answer(s): 135
