Multiple choice

Three friends P, Q and R have a certain amount of money with them in such a way that the ratio of amounts of money with P and Q is 3 : 4 and with Q and R is 5 : 6, respectively. If we multiply the amounts of money with Q and R, we get Rs. 5070 as the answer. Find the total amount of money (in Rs.) with all the friends.

  1. 155.75

  2. 190.50

  3. 191.75

  4. 195.50

  5. 197.75
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C Correct answer
Explanation

P:Q = 3:4, Q:R = 5:6. To combine, multiply P:Q by 5 and Q:R by 4: P:Q:R = 15:20:24. Let amounts be 15x, 20x, 24x. Q*R = 20x * 24x = 480x^2 = 5070. x^2 = 5070 / 480 = 10.5625. x = 3.25. Total = (15+20+24)x = 59x = 59 * 3.25 = 191.75.

AI explanation

Combining the ratios 3 to 4 and 5 to 6 gives a unified ratio of the amounts held by P, Q, and R as 15 to 20 to 24, meaning their amounts can be represented as 15x, 20x, and 24x. The product of the amounts of Q and R is 5070, so the equation is 20x multiplied by 24x equaling 480x squared, which simplifies to x squared equaling 10.5625 and x equaling 3.25. The total amount of money with all the friends is the sum of the ratio parts multiplied by x, which is 15 plus 20 plus 24 equaling 59, and 59 multiplied by 3.25 yields Rs. 191.75.

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