पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२८५

एतत् पृष्ठम् परिष्कृतम् अस्ति
89
CHAPTER V--RULE-OF-THREE.

An example on verse quadruple rule-of-three.

22. There is a block of stone (suited for building purposes), which measures 6 hastas in breadth, 30 hastas in length and 8 hastas in height, and (it is) 9 in worth. By means of this (given in exchange), how many (blocks) of such stone, fit to be used in building a Jina temple, (may be obtained, each) measuring 2 by 6 by 1 (hastas), and being 5 in worth?

Thus ends the inverse double, treble and quadruple rule-of-three.

The rule in regard to (problems bearing on associated) forward and backward movement.

28. Write down the net daily movement, derived from the difference of (the given rates of) forward and backward movements, each (of these rates) being (first) divided by its own (specified) time ; and then in relation to this (net daily movement), carry out the operation of the rule-of-three.

Examples in illustration thereof.

24-25. In the course of ${\displaystyle {\tfrac {3}{7}}}$ of a day, a ship goes over ${\displaystyle {\tfrac {1}{5}}}$ of a krōśa in the ocean; being opposed by the wind she goes back (during the same time) ${\displaystyle {\tfrac {1}{2}}}$— of a krōśa. Give out, O you who have powerful arms in crossing over the ocean of numbers well, in what time that (ship) will have gone over ${\displaystyle 99{\tfrac {2}{5}}}$ yōjanas.

26. A man earning (at the rate of) 1${\displaystyle 1{\tfrac {1}{4}}}$ of a gold coin in ${\displaystyle 3{\tfrac {1}{3}}}$ days, spends in ${\displaystyle 1{\tfrac {1}{2}}}$ days ${\displaystyle {\tfrac {1}{4}}}$ of the gold coin as also ${\displaystyle {\tfrac {1}{8}}}$ of that ${\displaystyle \left({\tfrac {1}{4}}\right)}$ itself; by what time will he own 70 (of those gold coins as his not earnings)?

27. That excellent elephant, which, with temples that are attacked by the feet of bees greedy of the (flowing) ichor, goes over ${\displaystyle {\tfrac {1}{5}}}$ as well as ${\displaystyle {\tfrac {1}{2}}}$ of a yōjana in ${\displaystyle 5{\tfrac {1}{2}}}$ days, and moves back in ${\displaystyle 3{\tfrac {1}{2}}}$ days over ${\displaystyle {\tfrac {2}{5}}}$ of a krōśa: say in what time he will have gone over (a net distance of) I00 yōjanas less by ${\displaystyle {\tfrac {1}{2}}}$ krōśa.

28-30.[28-30]A well completely filled with water is 10 daṇḍas depth a lotus sprouting up therein grows from the bottom

28-80.^ The 'depth' of the well is mentioned in the original as 'height' measured from the bottom of it.