Type 7: Fast Clock / āĻĻā§ā§°ā§āϤ āĻāĻĄāĻŧā§ (Fast Clock)
Q. A clock gains 2 minutes every hour. After 10 hours, it shows 12:00. What was the correct time ? (āĻāĻāύ āĻāĻĄāĻŧā§ āĻĒā§ā§°āϤāĻŋ āĻāĻŖā§āĻāĻžāϤ ⧍ āĻŽāĻŋāύāĻŋāĻ āĻāĻāĻŦāĻžāĻĸāĻŧā§āĨ¤ ā§§ā§Ļ āĻāĻŖā§āĻāĻžā§° āĻĒāĻŋāĻāϤ āĻāĻĄāĻŧā§āĻā§ā§ąā§ ⧧⧍:ā§Ļā§Ļ āĻĻā§āĻā§ā§ąāĻžāĻāĨ¤ āϤā§āύā§āϤ⧠āϏāĻ āĻŋāĻ āϏāĻŽāϝāĻŧ āĻāĻŋāĻŽāĻžāύ āĻāĻāĻŋāϞ ?)
Soln
The clock gains 2 minutes every hour. This means that after every real hour, the clock shows 2 minutes more than the actual time. (āĻāĻĄāĻŧā§āĻā§ āĻĒā§ā§°āϤāĻŋ āĻāĻŖā§āĻāĻžāϤ ⧍ āĻŽāĻŋāύāĻŋāĻ āĻāĻāĻŦāĻžāĻĸāĻŧā§āĨ¤ āĻ ā§°ā§āĻĨāĻžā§, āĻĒā§ā§°āĻā§āϤ ā§§ āĻāĻŖā§āĻāĻž āĻĒāĻžā§° āĻš'āϞ⧠āĻāĻĄāĻŧā§āĻā§ā§ąā§ ⧍ āĻŽāĻŋāύāĻŋāĻ āĻŦā§āĻāĻŋ āϏāĻŽāϝāĻŧ āĻĻā§āĻā§ā§ąāĻžāϝāĻŧāĨ¤)
Time passed = 10 hours, Clock gains = 2 minutes per hour
Clock Time = 12:00, Correct Time = Clock Time − Total Gain
= 12:00 − 20 minutes =11:40
āĻāĻĄāĻŧā§ā§° āϏāĻŽāϝāĻŧ = ⧧⧍:ā§Ļā§Ļ, āϏāĻ āĻŋāĻ āϏāĻŽāϝāĻŧ = āĻāĻĄāĻŧā§ā§° āϏāĻŽāϝāĻŧ − āĻŽā§āĻ āĻāĻāĻŦāĻĸāĻŧāĻž āϏāĻŽāϝāĻŧ
- Total Gain = Hours Passed × Gain per Hour (āĻŽā§āĻ āĻāĻāĻŦāĻĸāĻŧāĻž āϏāĻŽāϝāĻŧ = āĻĒāĻžā§° āĻšā§ā§ąāĻž āĻāĻŖā§āĻāĻž × āĻĒā§ā§°āϤāĻŋ āĻāĻŖā§āĻāĻžāϤ āĻāĻāĻŦāĻĸāĻŧāĻž āϏāĻŽāϝāĻŧ)
- Correct Time = Clock Time − Total Gain (āϏāĻ āĻŋāĻ āϏāĻŽāϝāĻŧ = āĻāĻĄāĻŧā§ā§° āϏāĻŽāϝāĻŧ − āĻŽā§āĻ āĻāĻāĻŦāĻĸāĻŧāĻž āϏāĻŽāϝāĻŧ)
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Practice Set – Fast Clock : Shortcut / āϏāĻšāĻ āύāĻŋāϝāĻŧāĻŽ
: āĻ āĻā§āϝāĻžāϏ⧰ āĻĒā§ā§°āĻļā§āύ – āĻĻā§ā§°ā§āϤ āĻāĻĄāĻŧā§
- A clock gains 1 minute every hour. After 8 hours, it shows 4:00 p.m. What is the correct time ? (āĻāĻāύ āĻāĻĄāĻŧā§ āĻĒā§ā§°āϤāĻŋ āĻāĻŖā§āĻāĻžāϤ ā§§ āĻŽāĻŋāύāĻŋāĻ āĻāĻāĻŦāĻžāĻĸāĻŧā§āĨ¤ ā§Ž āĻāĻŖā§āĻāĻžā§° āĻĒāĻŋāĻāϤ ā§Ē:ā§Ļā§Ļ āĻŦāĻāĻž āĻĻā§āĻā§ā§ąāĻžāϝāĻŧāĨ¤ āϏāĻ āĻŋāĻ āϏāĻŽāϝāĻŧ āĻāĻŋāĻŽāĻžāύ ?)
- A clock gains 2 minutes every hour. After 6 hours, it shows 3:00 p.m. What is the correct time ? (āĻāĻāύ āĻāĻĄāĻŧā§ āĻĒā§ā§°āϤāĻŋ āĻāĻŖā§āĻāĻžāϤ ⧍ āĻŽāĻŋāύāĻŋāĻ āĻāĻāĻŦāĻžāĻĸāĻŧā§āĨ¤ ā§Ŧ āĻāĻŖā§āĻāĻžā§° āĻĒāĻŋāĻāϤ ā§Š:ā§Ļā§Ļ āĻŦāĻāĻž āĻĻā§āĻā§ā§ąāĻžāϝāĻŧāĨ¤ āϏāĻ āĻŋāĻ āϏāĻŽāϝāĻŧ āĻāĻŋāĻŽāĻžāύ ?)
- A clock gains 3 minutes every hour. After 10 hours, it shows 8:00 p.m. What is the correct time ? (āĻāĻāύ āĻāĻĄāĻŧā§ āĻĒā§ā§°āϤāĻŋ āĻāĻŖā§āĻāĻžāϤ ā§Š āĻŽāĻŋāύāĻŋāĻ āĻāĻāĻŦāĻžāĻĸāĻŧā§āĨ¤ ā§§ā§Ļ āĻāĻŖā§āĻāĻžā§° āĻĒāĻŋāĻāϤ ā§Ž:ā§Ļā§Ļ āĻŦāĻāĻž āĻĻā§āĻā§ā§ąāĻžāϝāĻŧāĨ¤ āϏāĻ āĻŋāĻ āϏāĻŽāϝāĻŧ āĻāĻŋāĻŽāĻžāύ ?)
- A clock gains 4 minutes every hour. After 5 hours, it shows 12:00 noon. What is the correct time ? (āĻāĻāύ āĻāĻĄāĻŧā§ āĻĒā§ā§°āϤāĻŋ āĻāĻŖā§āĻāĻžāϤ ā§Ē āĻŽāĻŋāύāĻŋāĻ āĻāĻāĻŦāĻžāĻĸāĻŧā§āĨ¤ ā§Ģ āĻāĻŖā§āĻāĻžā§° āĻĒāĻŋāĻāϤ ⧧⧍:ā§Ļā§Ļ āĻŦāĻāĻž āĻĻā§āĻā§ā§ąāĻžāϝāĻŧāĨ¤ āϏāĻ āĻŋāĻ āϏāĻŽāϝāĻŧ āĻāĻŋāĻŽāĻžāύ ?)
- A clock gains 5 minutes every hour. After 12 hours, it shows 9:00 p.m. What is the correct time ? (āĻāĻāύ āĻāĻĄāĻŧā§ āĻĒā§ā§°āϤāĻŋ āĻāĻŖā§āĻāĻžāϤ ā§Ģ āĻŽāĻŋāύāĻŋāĻ āĻāĻāĻŦāĻžāĻĸāĻŧā§āĨ¤ ⧧⧍ āĻāĻŖā§āĻāĻžā§° āĻĒāĻŋāĻāϤ ⧝:ā§Ļā§Ļ āĻŦāĻāĻž āĻĻā§āĻā§ā§ąāĻžāϝāĻŧāĨ¤ āϏāĻ āĻŋāĻ āϏāĻŽāϝāĻŧ āĻāĻŋāĻŽāĻžāύ ?)
- A clock gains 6 minutes every hour. After 8 hours, it shows 7:00 p.m. What is the correct time ? (āĻāĻāύ āĻāĻĄāĻŧā§ āĻĒā§ā§°āϤāĻŋ āĻāĻŖā§āĻāĻžāϤ ā§Ŧ āĻŽāĻŋāύāĻŋāĻ āĻāĻāĻŦāĻžāĻĸāĻŧā§āĨ¤ ā§Ž āĻāĻŖā§āĻāĻžā§° āĻĒāĻŋāĻāϤ ā§:ā§Ļā§Ļ āĻŦāĻāĻž āĻĻā§āĻā§ā§ąāĻžāϝāĻŧāĨ¤ āϏāĻ āĻŋāĻ āϏāĻŽāϝāĻŧ āĻāĻŋāĻŽāĻžāύ ?)
- A clock gains 10 minutes every hour. After 6 hours, it shows 5:00 p.m. What is the correct time ? (āĻāĻāύ āĻāĻĄāĻŧā§ āĻĒā§ā§°āϤāĻŋ āĻāĻŖā§āĻāĻžāϤ ā§§ā§Ļ āĻŽāĻŋāύāĻŋāĻ āĻāĻāĻŦāĻžāĻĸāĻŧā§āĨ¤ ā§Ŧ āĻāĻŖā§āĻāĻžā§° āĻĒāĻŋāĻāϤ ā§Ģ:ā§Ļā§Ļ āĻŦāĻāĻž āĻĻā§āĻā§ā§ąāĻžāϝāĻŧāĨ¤ āϏāĻ āĻŋāĻ āϏāĻŽāϝāĻŧ āĻāĻŋāĻŽāĻžāύ ?)
- A clock gains 2 minutes every hour. After 12 hours, it shows 6:00 p.m. What is the correct time ? (āĻāĻāύ āĻāĻĄāĻŧā§ āĻĒā§ā§°āϤāĻŋ āĻāĻŖā§āĻāĻžāϤ ⧍ āĻŽāĻŋāύāĻŋāĻ āĻāĻāĻŦāĻžāĻĸāĻŧā§āĨ¤ ⧧⧍ āĻāĻŖā§āĻāĻžā§° āĻĒāĻŋāĻāϤ ā§Ŧ:ā§Ļā§Ļ āĻŦāĻāĻž āĻĻā§āĻā§ā§ąāĻžāϝāĻŧāĨ¤ āϏāĻ āĻŋāĻ āϏāĻŽāϝāĻŧ āĻāĻŋāĻŽāĻžāύ ?)