Practice Set: Profit & Ratio (HCF-LCM Type), Different Remainders





Different Remainders - Simple Trick


Q. Find the smallest number which gives remainders 14, 19 and 24 when divided by 20, 25 and 30.


Solution:


1st: Find the difference



  • 20 − 14 = 6

  • 25 − 19 = 6

  • 30 − 24 = 6


So, k = 6


2nd: Find LCM


LCM of 20, 25, 30 = 300


3rd: Subtract : 300 − 6 = 294 


Ans: 294


Formula: Number = LCM − Common Difference






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Practice Set: Profit & Ratio (HCF-LCM Type)

Questions



  1. If the ratio of two numbers is 3 : 4 and HCF = 5, find LCM.

  2. Ratio = 2 : 7, HCF = 3 → Find LCM.

  3. Ratio = 5 : 9, HCF = 4 → Find LCM.

  4. Ratio = 6 : 11, HCF = 2 → Find LCM.

  5. Ratio = 8 : 3, HCF = 7 → Find LCM.

  6. Ratio = 9 : 10, HCF = 6 → Find LCM.

  7. Ratio = 4 : 15, HCF = 5 → Find LCM.

  8. Ratio = 7 : 12, HCF = 3 → Find LCM.

  9. Ratio = 11 : 13, HCF = 2 → Find LCM.

  10. Ratio = 5 : 8, HCF = 9 → Find LCM.


Mixed Level



  1. Ratio = 3 : 5, HCF = 6 → Find both numbers and LCM.

  2. Ratio = 4 : 7, HCF = 8 → Find LCM.

  3. Ratio = 6 : 13, HCF = 3 → Find LCM.

  4. Ratio = 10 : 11, HCF = 2 → Find LCM.

  5. Ratio = 9 : 14, HCF = 5 → Find LCM.


Advanced (Exam Level)



  1. Two numbers are in ratio 7 : 9 and their HCF is 4. Find LCM

  2. Ratio = 8 : 15, HCF = 6 → Find LCM.

  3. Ratio = 12 : 5, HCF = 7 → Find LCM.

  4. Ratio = 13 : 17, HCF = 3 → Find LCM.

  5. Ratio = 11 : 6, HCF = 8 → Find LCM.


Trick (Remember) : LCM = HCF × (a × b)

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