Question
A motorboat whose speed is 20 km/h in still water takes
30 minutes more to go 24 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 2 km/h, then how much time will it take to go 39 km downstream and 30 km upstream?Solution
According to the question, the motorboat takes 30 minutes more to go 24 km upstream than to cover the same distance downstream. Let, the speed of the water = x km/h So, 24/(20 - x) = 24/(20 + x) + (1/2) [∵ 30 minutes = 1/2 hour] ⇒ 24/(20 - x) - 24/(20 + x) = (1/2) => {24(20+x) - 24(20-x)}/(400 - x2) = 1/2 => 24(20+x-20+x)/400 - x2 = 1/2 => (24 x 2x)/400-x2 = 1/2 ⇒ 400 - x2 = 96x ⇒ x2 + 96x - 400 = 0 ⇒ x2 + 100x - 4x - 400 = 0 ⇒ x (x + 100) - 4 (x + 100) = 0 ⇒ (x + 100) (x - 4) = 0 ⇒ x + 100 = 0 ⇒ x = -100 ["-" is neglacted] ⇒ x - 4 = 0 ⇒ x = 4 ∴ The speed of the water = 4 km/h The speed of the motorboat in still water increased 2 km/h = 20 + 2 = 22 km/h The time for 39 km downstream and 30 km upstream = 39/(22 + 4) + 30/(22 - 4) hours = (39/26) + (30/18) hours = 3/2 + 5/3 hours = 19/6 hours = (19/6) × 60 minutes = 190 minutes = 3 hours 10 minutes
A) Subdue B) Loose C) Stimulate D) Careless
Select the word which means the same as the group of words given.
Be harmonious or consistent with
The situation in which everything is happening in a confused way -
Select the word with the correct spelling.
What is the synonym for the word "acquiesce"?
 Fill in the blanks with the appropriate antonym of the word in Italic from the options given:
 The king was known for his generosity , but h...
She is known to be frank and always speaks her mind.
Select the INCORRECTLY spelt word.
Select the most appropriate synonym of the given word.Â
ESTIMATE
Choose the alternative which is closest to the opposite in meaning of the bold word in the sentence.
The scientist’s esoteric research was understo...