When ₹391 is divided into three parts in proportion to the fractions 1/2, 2/3, 3/4, then find its smallest part.
₹102
₹102 is correct.
The three parts are in the ratio \(\dfrac{1}{2} : \dfrac{2}{3} : \dfrac{3}{4}\). Multiplying each fraction by the LCM 12 gives whole numbers.
\(\dfrac{1}{2} \times 12 : \dfrac{2}{3} \times 12 : \dfrac{3}{4} \times 12 = 6 : 8 : 9\), so the total number of shares is \(6 + 8 + 9 = 23\).
One share = ₹\(391 \div 23 = 17\).
The smallest part has 6 shares = ₹\(6 \times 17 = 102\). The other parts are ₹136 and ₹153.
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