CTET Solved Paper - UPTET December 2016 Paper2
- Option : D
- Explanation : (D) Let the sped of the stream be 'x' km/h
Speed of the motor boat in still water = 15 km/h
∴ Speed of the motor boat in upstream = (15 - x) km/h
Speed of the motor boat in downstream = (15 + x) km/h
Total time take by the motor boat = 5h
Distance covered by motor boat in upstream = 36 km
Hence, distance covered by motor boat in downstream = 36 km
5(15 + x) (15 - x) = 36[15 -x + 15 + x]
5[(15)2 -x2] = 36 (30) [∵ (a + b)(a - b) = a2 - b2]
(225 -x2) = 36 × 6 225 - 216 = x2
x 2 = 9
x = 3 km/h (speed of the stream)
149. The sum of two natural number is 8. Determine the numbers if the sum of their reciprocals is 
- Option : A
- Explanation : (A) Let the two numbers be x and (8 - x)
Then,
⇒ 15 × 8 = 8x(8 - x)
⇒ 120 = 64x - 8x2
⇒ 8x2 - 64x + 120 = 0
⇒ x2 - 8x + 15 = 0
⇒ x2 -5x - 3x + 15 = 0
⇒ x(x - 5) - 3(x - 5) = 0
⇒(x - 3) (x - 5) = 0
⇒ x = 3, 5
Hence, the two natural numbers are 3 and 5
150. The ratio of two numbers is 5:6 and their HCF is 12. Their LCM is
- Option : D
- Explanation : (D) Let the two numbers be 5x and 6x
∵ HCF of 5x and 6x is 12
∴ Number are 5 × 12 = 60
and 6 × 12 = 72
LCM of 60 and 72 is
LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 = 360
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