Multiple choice

Divya and Sneha together has Rs. $55$. If $\dfrac14$ of divya's share is equal to $\dfrac16$ of Sneha's share. What would be the difference of their amount?

  1. Rs. $16$
  2. Rs. $18$
  3. Rs. $11$
  4. Rs. $15$
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C Correct answer
Explanation

Let Divya's share be D and Sneha's share be S. We are given that D + S = 55 and D/4 = S/6, which simplifies to the ratio D/S = 2/3. This means their shares can be written as 2k and 3k, and solving 2k + 3k = 55 gives k = 11. The difference between their shares is S - D = k = 11.

AI explanation

Assume Divya's share is x and Sneha's share is y, leading to the two equations x plus y equals 55 and x divided by 4 equals y divided by 6. Using the second equation, you find that x equals two-thirds of y, and substituting this into the first equation gives five-thirds of y equals 55, meaning y is 33. Since x plus y equals 55, x must be 22, and the difference between their amounts is 33 minus 22, which equals 11.

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