Multiple choice

Divide Rs. 4,260 into three parts proportional to $\displaystyle {2\frac{1}{2}\, :\, 1\frac{2}{3}\, :\, 1\frac{3}{4}}$.

  1. Rs. $1,800$ ;  Rs.$1,200$ and Rs.$1,260$
  2. Rs.$1,600$ ; Rs.$1,200$ and Rs.$1,260$
  3. Rs.$1,800$ ; Rs.$1,200$ and Rs.$1,280$
  4. Rs.$1,800$ ; Rs.$1,400$ and Rs.$1,260$
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A Correct answer
Explanation

Ratios are 5/2 : 5/3 : 7/4. Multiply by LCM(2,3,4)=12 to get 30 : 20 : 21. Total parts = 71. 4260 / 71 = 60. Parts are 30*60=1800, 20*60=1200, 21*60=1260.

AI explanation

Convert the mixed numbers to improper fractions to get the ratio 5/2 : 5/3 : 7/4. Multiplying by the least common multiple of 2, 3, and 4, which is 12, gives the simplified whole number ratio of 30 : 20 : 21. The sum of these ratio parts is 71, and multiplying the fraction 30/71 by the total amount of Rs. 4,260 yields Rs. 1,800 for the first part. Similarly, multiplying 20/71 by 4,260 gives Rs. 1,200 for the second part, and multiplying 21/71 by 4,260 gives Rs. 1,260 for the third part.

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