Q. 213.7( 3 Votes )

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Answer :

Jenny will use the club every alternate day


So, the series of the days Jenny uses the club = 1, 3, 5, 7, 9 .... 359


Let the number of days Jenny used the club be 'x'


an = a + (n–1) d


359 = 1 + (x–1) 2


359 – 1 = 2x – 2


358 + 2 = 2x


2x = 360


x = 180 days


Sally will use the club every third day.


So, the series of days Sally uses the club = 1, 4, 7, 10, 13 .....358.


Let the number of days Sally used the club be 'y'.


an = a + (n–1) d


358 = 1 + (y–1) 3


358 – 1 = 3y – 3


357 + 3 = 3y


360 = 3y


y = 120.


Every sixth day both Jenny and Sally use the club together,


So, the series of days when both Jenny and Sally use together = 1, 7, 13, 19.... 355.


Let the total number of days when both Jenny and Sally will go to the club together be 'B'.


an = a + (n–1) d


355 = 1 + (B–1) 6


355 – 1 = 6B – 6


354 + 6 = 6B


360 = 6B


B = 60


So, total number of days they both went to the club = x + y – B


180 + 120 – 60


300 – 60 = 240


So, the number of days when none of them went to the club = 360 – 240 = 120 days.


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RS Aggarwal - Mathematics