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Question

The red and yellow lights hanging on a Christmas tree flash at regular intervals. The red lights flash 10 times every 100 seconds and the yellow lights flash 8 times 150 seconds. After a period of time had passed, the red light had 252 more times than the yellow light. How many times did both the red and yellow lights flash over that period of time?

Answer

Method 1 :
For every 150sec,
red : 15
yellow : 8
15 – 8 = 7
252/7 = 36
36 x (15 + 8) = 828

Method 2 :
LCM of 100 and 150 is 300
For every 300s,
red : 10 x 3 = 30
yellow : 8 x 2 = 16
30 – 16 = 14
252/14 = 18
18 x (16 + 30) = 828

Ans : 828 times.

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This is a Quantity Each Product question. 

100/10 = 10

150/8 = 18.75

      Quantity  Each  Product   
Red 1u +252 10 10u + 2520  
Yellow  1u 18.75 18.75u  
 Total  2u + 252      

10u + 2520 = 18.75u

2520 = 18.75u – 10u

8.75u = 2520

1u = 2520 ÷ 8.75 =  288

2u = 288 × 2 = 576

576 + 252 = 828

 

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