As we know that ,
Present worth = Amount ? True Discount = 110 ? 10 = Rs. 100
SI on Rs. 100 for a certain time = Rs. 10
SI on Rs. 100 for double the time = Rs. 20
True Discount on Rs. 120 = 120 ? 100 = Rs. 20
True Discount on Rs. 1 = 20/120
True Discount on Rs. 440 = 20 x 440/120 = 20 x 44/12 = 20 x 22 / 6 = 440 /6 = 73.2
Given in the question ,
PW of Rs. 12,880 due 8 months hence = Rs. 11500; Clearly 12000 in cash is a better offer.
Rate in still water=[(1/2)(u+v)] km/h
Rate of current=[(1/2)(u-v)] km/h
where u= speed of boat in downstream
v=speed of boat in upstream
Speed of boat in still water=[(1/2)(7+13)] =10 km/h
Speed of the stream =[(1/2)(13-7)]=3 km/h
Let the speed of the stream = x km/h
?Speed of boat in still water = 10 km/h
Speed of boat downstream = ( x + 10) km/h
Speed of boat upstream=(10 - x) km/h
? Time taken to travel 26 km downstream=[ 26 / ( 10 + x ) ] h
Time taken to travel 14 km upstream=[ 14 /( 10 - x )] h
? By condition [ 26 / ( 10 + x)]=[ 14 / ( 10 - x)]
? 26(10-x)=14(10+x)
? 260-26x =140 + 14x
? 40x=120
? x = 3 Here, speed of stream = 3 km/h
Speed upstream = (40/8) km/hr = 5 km/hr
Speed downstream = (36/6) km/hr = 6 km/hr
Speed of boat in still water = (5 + 6)/2 km/hr = 5.5 km/hr.
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