Subject
Quantitative Aptitude
Topic
Miscellaneous
There are two vessels, one containing 12 litres of water, the other 6 litres of wine. If a litre be taken out of each and poured into the other, and if this be repeated four times, find how much wine will be in container one?
There are two vessels, one containing 12 litres of water, the other 6 litres of wine. If a litre be taken out of each and poured into the other, and if this be repeated four times, find how much wine will be in container one?
ক)
9.27 litreখ)
2.73 litreগ)
3.27 litreঘ)
4.00 litreঙ)
5.05 litreExplanation
Initial volumes of first and second vessel = 12 and 6 litres Formula to be used, Volume of wine after exchange in the first vessel = Volume of wine in first vessel before this exchange –(1 × fractional volume of wine in the first vessel during the exchange) + (1 × fractional volume of wine in the second vessel during the exchange) Volume of wine after exchange in the second bottle = Volume of wine in second vessel before this exchange – (1 × fractional volume of wine in the second vessel during the exchange) + (1 × fractional volume of wine in the first vessel during the exchange) After first exchange, volume of wine in the first vessel = 0 – 0 + 1 × 1 = 1litre ∴fractional volume of wine in the first vessel = 1/12 Volume of wine remaining in the second vessel = 6 – 1 × 1 + 0 = 5litres ∴fractional volume of wine in the second vessel = 5 / 6 After 2nd exchange, Volume of wine in the first vessel = 1 – 1 × 1 /12 + 1 × 5 / 6 = 21 / 12 litres ∴fractional volume of wine in the first vessel = (21 / 12)/12 = 21 / 144 Volume of wine in the second vessel = 5 – 1 × 5 / 6 + 1 × 1 / 12 = 51 / 12 litres ∴fractional volume of wine in second vessel = ( 51 / 12 ) / 6 = 51 / 72 After 3rd exchange, Volume of wine in the first vessel = 21 / 12 – 1 × 21 /144 + 1 × 51 /72 = 37 / 16 litres ∴fractional volume of wine in first vessel = (37 / 16) /12 = 37 / 192 Volume of wine in the second vessel = 51 / 12 – 1 × 51 / 72 + 1 × 21 / 144 = 59 /16 ∴fractional volume of wine in second vessel = ( 59 / 16 ) / 6 = 59 / 96 After 4thexchange, Volume of wine in the first vessel = 37 / 16 – 1 × 37 / 192 + 1 × 59 / 96 = 175 / 64 = 2.734 ∴volume of wine in the first vessel after 4 exchanges = 2.734Related questions
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