Divide 62 into two parts such that fourth part of the first and two fifth part of the second are in the ratio of 2:3
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Let the two parts be x and y. We have, x + y = 62 ...
(1) From the second condition, we have
(x/4)/(2y/5) = 2/3 3x/4 = 2(2y/5) 15x = 16y 15x – 16y = 0 ...
(2) Multiplying equation (1) by 15, we get 15x + 15y = 930 ...
(3) Subtracting equation (2) from equation (3) we get 31y = 930 ⇒ y = 930/31 = 30 Putting y = 30 in equation (1), we get x + 30 = 62 ⇒ x = 62 – 30 = 32 Hence, the two parts of 62 are 32 and 30.
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