Sher Singh bought some oranges and apples .Oranges were brought at 7 for Rs 50 and apples at 5 for Rs 30 . If sher Singh spent an equal amount of money on the apples and oranges , what was the least number of fruits he bought ?

Options

A. 12
B. 21
C. 25
D. 46

Answer

To solve the problem, we need to determine the least number of fruits Sher Singh bought, given that he spent an equal amount on oranges and apples.

### Step 1: Determine the cost per fruit for oranges and apples.
- Oranges: 7 for Rs 50
- Cost per orange = 50 / 7 = Rs 7.14 (approximately)

- Apples: 5 for Rs 30
- Cost per apple = 30 / 5 = Rs 6

### Step 2: Let the amount spent on oranges and apples be the same.
Let the amount spent on oranges be Rs x and the amount spent on apples also be Rs x.

### Step 3: Calculate the number of oranges and apples bought.
- Number of oranges bought = x / (50 / 7) = (7x) / 50
- Number of apples bought = x / (30 / 5) = (5x) / 30 = (x / 6)

### Step 4: Find a common value for x that results in whole numbers of fruits.
To find the least number of fruits, we need to ensure that both (7x)/50 and (x/6) are whole numbers.

1. For (7x)/50 to be an integer, x must be a multiple of 50.
2. For (x/6) to be an integer, x must be a multiple of 6.

### Step 5: Find the least common multiple (LCM) of 50 and 6.
- The prime factorization of 50 is 2 × 5².
- The prime factorization of 6 is 2 × 3.

The LCM is obtained by taking the highest power of each prime:
- LCM = 2¹ × 3¹ × 5² = 150.

### Step 6: Calculate the number of fruits for x = 150.
- Number of oranges = (7 * 150) / 50 = 21.
- Number of apples = (150 / 6) = 25.

### Step 7: Calculate the total number of fruits.
Total fruits = Number of oranges + Number of apples = 21 + 25 = 46.

### Final Answer:
The least number of fruits Sher Singh bought is **46**.

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