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! !Failed!in!Mathematics!=!100L65!=!35%! 57.$$SI!=! <//$B$.#$B$D$ !=!960t!⇒!A!=8000!+!960t!
! !Fail!in!both!subjects!=!15%! .//
!!!!!!Total!fail!=A+BLC!=25!+!35!L15!=!45%! !!!!!!!!!!!!Again,!!SI! ,.//$B$./$B$D$ !=!910t!
!!!!!!Total!number!of!students!in!the!exam!! .//
.// !!!!!!!A!=!9100!+!910t!
!!!!!!=! !x!!!495!=!1100$
7-$ !!!!!!!According!to!the!question,!!
$ !!!!!!!960t!+!8000!=!910t!+!9100⇒50t!=!1100!
51.!!Net!effect!=! (.//9.-)(.//;#/)$ ! ! ! t!=! ..//$ !=!22$yr$
.//
! =! ..-$"$</$ !=!23!x!4!=!92! $ -/
.//
! Loss!=!8%! 58.$Let rate = R% and time = R years.
52.!! Let! the! amount! of! water! to! be! added! Then, 1200 x R x R = 432
be!xx!liters.!! 100
! 12R = 432

2
2
We!want!the!percentage!of!water!to!increase!from! R = 36
10%! to! 20%! or! percentage! of! nonLwater! to! R = 6.
decrease! from! 90%! to! 80%.! Note! that! when! we! 59.!!!Let!the!number!=!x.! "$
add!xx!liters! of! water! the! amount! of! nonLwater! in! !!!!!!!!∴$Correct!answer!=!! !!
mixture! in! liters! remains! the! same,! so:! !!!!!!!!!!!!!!!!!!!!!!3x!=!29.7! 0
! #,.1$
0.9∗40=0.8(40+x)0.9∗40=0.8(40+x)!LL>!x=5x=5.! !!!!!!!!!!!!!x!=! !=!9.9!
! 0 ,.,$
53.!!Let!numbers!be!3x!4x!and!5x! !!!!!!!!!∴$Correct!answer!=!! 0 !=!3.3!
#$
#$$
#$
!!!!!!!9% +16% +!25% !=!1250!
!!!!!!!!⇒!!!!!!!!!!!!!!!!!59x 2!!=! 1250!
!!!!!!!!⇒!!!!!!!!!!!!!!!!!!!!!x 2!!!=!25! , .1 #< 00
!!!!!!!!⇒!!!!!!!!!!!!!!!!!!!!!x!!!!=!5! 60.!!! ,! ,! ,! !
.0 #G 0, -#
!!!!!!!!Numbers!are!15,!20!and!25! !!!!!!!!LCM!of!13,!26,!39!and!52!=!156!
!!!!!!!!∴!!!!sum!of!numbers!=!15+20!and!25!=!60$ $ .#$B$,,./#,..#,,,
! !!!!!!!!∴! .-G !
54.!!!Total!age!of!3!boys!=!25x!3!=!75!yr! ./<,$$$./#,..#,,,
!!!!!!!!!3x!+!5x!+!7x!=!75!⇒15x!=75!⇒!!x!=!5! !!!!!!!!∴! .-G !
VV
!!!!!!!!!Smallest!age=!3!x!5!=15$yrs!! !!!!!!!!∴ $IJKLLMNO$PQKROSTU$!$ $
! WX
$ !!!!!! 19$
$ !!!!!!!!!1!!!!!!!!!4!!!!!!!!!7!!!!!!!!!10!!!!!!!!13!!!!!!16!!!!!!!!!
55.$$Let!number!of!hens=!x!and!number!of!cows=y! !
$$$$$$$∴!!!!!!!!!x!+!y!=!48! 84.!!
$$$$$$$and!!2x!+!4y=140! ! !!!!+3!!!!!!+3!!!!!!!+3!!!!!!!!+3!!!!!!!!+3!!!!!+3!
!!!!!!!Solving!(i)!and!(ii),!we!get!x!=!26,!y!=22! !!!!!!!!!!
!!!!!!!∴!Number!of!hens!=!26! Hence,!required!answer!is!19$
! ! 21$
56.!Let!P!=!₹x!⇒!A!=!₹!3x! !!!!!!!!0!!!!!!!!!!1!!!!!!!!!3!!!!!!!!!!6!!!!!!!!10!!!!!!15!!!!!!!!!
!!!!!!SI!=ALP=3x!–x!=!₹!2x! !
@A$B$.//$ #"$B$.//$ 85.!!
!!!!!!∴!r!= !=! !=!10$ !!!!!!!!!!!!!!!+1!!!!!!+2!!!!!!!+3!!!!!!!!+4!!!!!!!+5!!!!!!+6!
C$B$D "$B$#/
!!!!!! !!!!!!!!!Hence,!required!answer!is!21!
nd
!!!!!!2 !Case!P!=!₹x!⇒A!=₹!2x! !
!!!!!!SI!=!2x!–!x!=!x! ! 22$
!!!!!!r!=!10%! !!!!!!!!36!!!!!!!!34!!!!!!30!!!!!!!!28!!!!!!!!24!!!!!!!!!!!!!!!
@A$B$.//$ "$B$.//$ !
!!!!!!t!=! !=! !=!10$$ 86.!!
C$B$E "$B$./
$ !!!!!!!!!!!!!!!L2!!!!!!!L4!!!!!!!!L2!!!!!!!!!L4!!!!!!!!!L2!
!!!!!!!!!Hence,!required!answer!is!22$

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