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Hints*and*Solutions$$

Q.$No$
$ ' e%f '= d '=' ]bg%dg '
41.' Let'the'number'='x' e*g ]bg ]bg*dg
' X '='(37) '–'(23) ='(37'+'23)'(37'@23)' ' '
2
2
2'
)i
' ⇒'x ='60'X'14' = c]g '=' '
2'
''''''''''''''⇒'x ='840'⇒'x'=' 840'='28.98' ' hg #
2'
' ''''''' 46.' Let'798'='a'and'579'='b'
2' 840' 28.98' (e%g') '*'(e*g') '
j
j
4' ' ∴' '
48' 440' ' ' e'k'g'
384' j j j j
569' 5600' ' ' ' =' e %ceg%g *'e *'g %ceg' '
5121' eg
' 47800' ' ' ' =! ^eg' !=!4"
eg
46304' 47."A'man's'average'monthly'expenditure'for'the'
' 1586' ' first'four'months'of'the'year'was'Rs.231.25.''
' He'spent'231.25'X'4'='Rs.'925''
42.' Let'the'average'age'of'8'men'be'x'yr' For'the'next'five'months',the'average'monthly'
' Sum'of'ages'of'8'men'='8x'yr' expenditure'was'Rs.'22.75'more'than'what'it'was'
' Age'of'7'men'+'30'yr'='8x'yr' during'the'first'four'months.''
' In'the'second'case,' He'spends'231.25+22.75'for'one'month''
' '''Average'age'of'8'men'=(x'+'4)'yr' In'5'months'he'spends'(231.25+22.75)'X'5'='1270''
' ' Total'age'of'8'men'='8(x'+'4)' If'the'person'spent'Rs.605'in'all'during'the'
' ⇒'Age'of'7'men+'Age'of'new'man' remaining'three'months'of'the'year,'
' ' ='8x'+'32' Total'expense'='925+1270+605='2800''
' Subtract'Eq.'(i)'from'Eq.'(ii),'we'get' Saving'='3500@2800'='700''
' ' 7'men'+'Age'of'new'man'@7'men@30' %'saving'='700/3500'X'100'='20'%'
' ' ='8x'+'32'–'8x' '
' ∴'Age'of'new'man'='32'+'30'='62'yr'
' 48.' let x = number of girls and y = number of boys
43.' Let'weight'of'empty'vessel'='y'kg' sum of girls ages / x = 15.4
' According'to'the'question,' sum of boys ages / y = 16.4
' ' x'+'y'='24' The sum of the girls' ages is 15.4x,
' ' ] '(x)'+'y'='9' and boys' sum is 16.4y
^ (sum of girls ages+sum of boys ages)/(x+y)= 15.8
' ' x'+'y'='24'
' ' x'+'4y'='36' (15.4x + 16.4y) / (x+y) = 15.8
''''''''''''Solving'Eqs.'(i)'and'(ii)'we'get'y=4'and'x=20' 15.4x + 16.4y = 15.8(x+y)
' ∴''Weight'of'empty'vessel'='4'kg' 15.4x + 16.4y = 15.8x + 15.8y
' 0.6y = 0.4x
44.'' We'have'a'@'b'='and'ab'='45' 0.6y/x = 0.4
' Then,'value'of'a 'b '=(a'@'b) '+'3ab(a'+'b)' y/x = 0.4/0.6 = y : x = 2/3
3
3'–
3
' ' ='(4) '+'3'(45)'(4)' Hence, ratio of boys : girls = 2:3'
3
' ' ='64'+'540'='604' ]r's'r
' 49."""Number!of!bucket!= ]c !=!12!
` ]b 50."""Let!P!=!₹!100!
45.' '= '⇒21a'='15a'+'15b'
`%a c] st ]tt'u'r'u']
' ⇒' ' 6a'='15b' ! In!1 !case,!SI!=! ]tt '=!₹!8!
' nd ]tt'u']c'u']
]b ! In!2 !case,!SI!=! '=!₹!12!
' ⇒' ' ''a''=' b' ]tt
d
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