If 152 is divided into four parts proportional to 3, 4, 5 and 7, then the smallest part is
24
To solve the problem of dividing 152 into four parts proportional to 3, 4, 5, and 7, we need to use the concept of ratios.
The given ratios are 3, 4, 5, and 7. Let's assume these parts are represented by \(3x\), \(4x\), \(5x\), and \(7x\) respectively.
The sum of these parts equals the total, which is 152. Therefore, we can write the equation:
\(3x + 4x + 5x + 7x = 152\)
\((3 + 4 + 5 + 7)x = 152\)
\(19x = 152\)
Solving for \(x\), we get:
\(x = \frac{152}{19}\)
Upon simplifying, \(x = 8\).
Now, we can find the parts:
- First part: \(3x = 3 \times 8 = 24\)
- Second part: \(4x = 4 \times 8 = 32\)
- Third part: \(5x = 5 \times 8 = 40\)
- Fourth part: \(7x = 7 \times 8 = 56\)
Therefore, the smallest part is 24.
This matches the provided option 24, which is the correct answer.
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Important Questions from Ratio and Proportion
- A box containing the denominations of one rupee coins, five rupee coins and ten rupee coins amount to Rs.4320. There are equal number of
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- A box containing the denominations of fifty paise coins, two rupee coins and five rupee coins amount to Rs. 1275. There are equal number of coins in all denominations. What is the value of two rupee coins in the box? (In Rs.)
- Three numbers are in the ratio 19:21:23. If the difference between thrice the third number and the sum of first and second number is 841. Find the difference between the first and third number?
- The ratio between the number of males and females in a college is 27:28. If the number of males are increased by 20% and the number of females are increased by 30%, then what will the new ratio of males and females in the college?
