Question : If Ram’s income exceeds Shyam’s income by 70% and Shyam’s income is less than Sohan’s income by 30%, then find the ratio of the incomes of Ram and Sohan.
Option 1: 119 : 100
Option 2: 121 : 102
Option 3: 120 : 101
Option 4: 118 : 99
Correct Answer: 119 : 100
Solution : Given: Ram’s income exceeds Shyam’s income by 70% and Shyam’s income is less than Sohan’s income by 30%. Let R, S, and H be Ram, Shyam, and Sohan's income respectively. Now, R = S + 0.7S = 1.7H and S = H - 0.3H = 0.7H So, R = 1.7S ⇒ R = 1.7(0.7H) ⇒ R = 1.19H So, R : H = 1.19H : H = 119 : 100 Hence, the correct answer is 119 : 100.
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