Three search lights flash at intervals of 20 s, 30 s and 45 s. The time…
2011
Three search lights flash at intervals of 20 s, 30 s and 45 s. The time between two simultaneous flashes is
- A.
5 s
5 से - B.
90 s
90 से - C.
120 s
120 से - D.
180 s
180 से
Attempted by 12 students.
Show answer & explanation
Correct answer: D
To find the time between two simultaneous flashes, we need to calculate the least common multiple (LCM) of the intervals: 20 s, 30 s, and 45 s.
Step 1: Prime factorization of the numbers: - 20 = 2² × 5 - 30 = 2 × 3 × 5 - 45 = 3² × 5
Step 2: Take the highest powers of all prime factors: - 2², 3², 5 → LCM = 4 × 9 × 5 = 180 s
Step 3: Verify that 180 s is divisible by all three intervals: - 180 ÷ 20 = 9 (whole number) - 180 ÷ 30 = 6 (whole number) - 180 ÷ 45 = 4 (whole number)
Thus, the time between two simultaneous flashes is 180 s.
हिन्दी उत्तर:
दो युगपत् दीप्तों के बीच का समय तीनों अंतरालों का लघुत्तम समापवर्त्य (LCM) होता है। 20, 30 और 45 का LCM निकालने पर 180 सेकंड प्राप्त होता है।
इसलिए, दो युगपत् दीप्तों के बीच का समय 180 सेकंड है।