21. A pile of mangoes was collected. The king took one-sixth, the queen one-fifth of the remainder, the three princes one-fourth, one-third, and one-half of the successive remainders, and the youngest child took the three remaining mangoes. Find the number of mangoes in the pile. (Mahavira) 22. The total cost of nine citrons and seven fragrant wood apples is 107 coins; the cost of seven citrons and nine fragrant wood apples is 101 coins. Find the cost of a citron and a wood apple. (Mahavira)
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History Solve this problem, which was posed by Mahavira, an Indian mathematician who lived around 850 A.D. The mixed price of 9 citrons and 7 fragrant wood apples is 107 ; again, the mixed price of 7 citrons and 9 fragrant wood apples is $101 . O$ you Arithmetician, tell me quickly the price of a citron and of a wood apple here, having distinctly separated those prices well.
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Solving Systems of Equations
A man bought 50 dozen fruits consisting of apples and bananas. An apple is cheaper than a banana. The number of dozens of apples he bought is equal to the cost per dozen of bananas in rupees and vice versa. If he had spent a total amount of $\mathrm{Rs} 1050$, find the number of dozens of apples and bananas he bought respectively. (1) 12 and 38 (2) 14 and 36 (3) 15 and 35 (4) 18 and 32
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