If 76 is divided into the ratio of 7:5:3:4, then the smallest part will be

Question

Accepted Answer

The correct option is 1:
To divide a quantity into a given ratio, we first need to find the sum of the ratio parts. Then, we divide the total quantity by this sum to find the value of one 'share' or 'unit' of the ratio. Finally, we multiply this unit value by each part of the ratio to find the individual parts, and identify the smallest among them.

Step 1: Find the sum of the ratio parts.
The given ratio is $7:5:3:4$.
Sum of the ratio parts $= 7 + 5 + 3 + 4 = 19$.

Step 2: Divide the total quantity by the sum of the ratio parts to find the value of one share.
The total quantity to be divided is $76$.
Value of one share $= \frac{	ext{Total quantity}}{	ext{Sum of ratio parts}} = \frac{76}{19} = 4$.

Step 3: Multiply the value of one share by each part of the ratio to find the individual parts.
First part $= 7 	imes 4 = 28$.
Second part $= 5 	imes 4 = 20$.
Third part $= 3 	imes 4 = 12$.
Fourth part $= 4 	imes 4 = 16$.

Step 4: Identify the smallest part.
The parts are $28, 20, 12, 16$.
The smallest part is $12$.

Therefore, the smallest part when 76 is divided into the ratio of $7:5:3:4$ is $12$.

The incorrect option is 2: 20
This would be the second smallest part, corresponding to the ratio part of 5.

The incorrect option is 3: 16
This would be the third smallest part, corresponding to the ratio part of 4.

The incorrect option is 4: 10
This value is not obtained when dividing 76 in the given ratio. A common mistake might be an arithmetic error in calculating the parts or the sum of the ratio. If one share was incorrectly calculated as 2.5 (e.g., if the sum of ratios was thought to be 28, then 76/28 is approximately 2.7, or if the smallest ratio part was incorrectly multiplied by a different share value), it could lead to incorrect numbers.