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Ram, Shyam,Tarun and Varun together had a total amount of Rs. 240 with them. Ram had half of the total amount with the others. Shyam had one-third of the total amount with the others. Tarun had one-fourth of the total mount with the others. Find the amount with varun (in Rs.). A) 78 B) 69 C) 52 D) 92 |
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Answer» Correct option is (C) 52 Let Ram, Shyam, Tarun and Varun had amount of Rs x, y, z and w respectively. \(\because\) They had a total amount of Rs 240 together. \(\therefore\) x+y+z+w = 240 ______________(1) According to other given conditions, we have \(x=\frac{y+z+w}2\) \(\Rightarrow\) y+z+w = 2x ______________(2) \(y=\frac{x+z+w}3\) \(\Rightarrow\) x+z+w = 3y ______________(3) and \(z=\frac{x+y+w}4\) \(\Rightarrow\) x+y+w = 4z ______________(4) From (1) & (2), we obtain x+2x = 240 \(\Rightarrow\) 3x = 240 \(\Rightarrow\) x = 80 From (1) & (3), we obtain y+3y = 240 \(\Rightarrow\) 4y = 240 \(\Rightarrow\) y = 60 From (1) & (4), we obtain z+4z = 240 \(\Rightarrow\) 5z = 240 \(\Rightarrow\) z = \(\frac{240}5\) = 48 Put x = 80, y = 60, z = 48 in (1), we get 80+60+48+w = 240 \(\Rightarrow\) w = 240 - 188 = 52 Hence, the amount which Varun has Rs 52. Correct option is C) 52 |
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