Multiple choice

The total of the daily wages of Ram, Shyam and Mohan is $Rs. 450$. If they, respectively spend $25\%, 20\%$ and $50\%$ of their incomes then the ratio of their savings becomes $9 : 8 : 4$. What is the income of Ram?

  1. $180$
  2. $190$
  3. $200$
  4. $175$
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A Correct answer
Explanation

Let incomes be R, S, M. R+S+M = 450. Savings: R(1-0.25)=0.75R, S(1-0.20)=0.8S, M(1-0.5)=0.5M. Ratio 0.75R : 0.8S : 0.5M = 9:8:4. 0.75R/9 = 0.8S/8 = 0.5M/4 = k. R=12k, S=10k, M=8k. 12k+10k+8k=450 -> 30k=450 -> k=15. R = 12*15 = 180.

AI explanation

Let the total incomes of Ram, Shyam, and Mohan be R, S, and M. Their savings are 75% of R, 80% of S, and 50% of M, meaning their savings ratio is 0.75R : 0.80S : 0.50M, which equals 9 : 8 : 4. Equating the ratio parts gives 0.75R = 9y, 0.80S = 8y, and 0.50M = 4y; solving these yields R = 12y, S = 10y, and M = 8y. The total income is 12y + 10y + 8y = 30y, which equals Rs. 450, so y = 15. Ram's income is 12y, which is 12 multiplied by 15, giving Rs. 180.

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