1.If (p,q) is the solution of the simultaneous equations 1/x - 5/y=38 and 5/x + 2/y=1,then find the value of p+q.
 
2.In a bag,there are some notes in the denominations of Rs.20,Rs.5 & Rs.10.The total no. of notes is 20 and their total value is Rs.175.The no. of Rs.5 notes is equal the no. of notes of exactly one of the other denomination.Find this denomination.
 
3.The length and the breadth of a rectangle are integers (in cm).Its perimeter is 24 cm.Its area is at least 30 sq cm.How many different rectangles exist?
 
4.If 1/2-x + 1/10+x=1/8+x + 1/4-x,then find the value of x. 

Asked by smanishkumar2002 | 1st Oct, 2015, 09:33: PM

Expert Answer:

1. C o n s i d e r space t h e space s y s t e m space o f space e q u a t i o n s 1 over x minus 5 over y equals 38.. left parenthesis 1 right parenthesis 5 over x plus 2 over y equals 1... left parenthesis 2 right parenthesis N o w space s u b s t i t u t i n g space 1 over x equals u space a n d space 1 over y equals v comma space w e space h a v e comma u minus 5 v equals 38... left parenthesis 3 right parenthesis 5 u plus 2 v equals 1... left parenthesis 4 right parenthesis M u l t i p l y i n g space e q u a t i o n space left parenthesis 3 right parenthesis space b y space 2 space a n d space e q u a t i o n space left parenthesis 4 right parenthesis space b y space 5 comma space w e space h a v e comma 2 u minus 10 v equals 76... left parenthesis 5 right parenthesis 25 u plus 10 v equals 5... left parenthesis 6 right parenthesis A d d i n g space e q u a t i o n s space left parenthesis 5 right parenthesis space a n d space left parenthesis 6 right parenthesis comma space w e space h a v e comma 27 u equals 81 rightwards double arrow u equals 3 S u b s t i t u t i n g space t h e space v a l u e space u equals 3 space i n space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e comma 3 minus 5 v equals 38 rightwards double arrow negative 5 v equals 38 minus 3 rightwards double arrow v equals negative 35 rightwards double arrow v equals fraction numerator negative 35 over denominator 5 end fraction equals negative 7 T h u s comma space u equals 3 space a n d space v equals negative 7 rightwards double arrow 1 over x equals 3 space a n d space 1 over y equals negative 7 rightwards double arrow x equals 1 third space a n d space y equals fraction numerator negative 1 over denominator 7 end fraction G i v e n space t h a t space p space a n d space q space a r e space t h e space s o l u t i o n comma space w e space h a v e comma p equals 1 third space a n d space q equals fraction numerator negative 1 over denominator 7 end fraction T h u s comma space p plus q equals 1 third plus open parentheses fraction numerator negative 1 over denominator 7 end fraction close parentheses equals fraction numerator 7 minus 3 over denominator 21 end fraction equals 4 over 21  3. L e t space l space a n d space b space b e space t h e space l e n g t h space a n d space t h e space b r e a d t h space o f space a space r e c tan g l e. G i v e n space t h a t space i t s space p e r i m e t e r equals 24 space c m rightwards double arrow 2 open parentheses l plus b close parentheses equals 24 rightwards double arrow l plus b equals 12... left parenthesis 1 right parenthesis A l s o space g i v e n space t h a t space A r e a equals 30 space s q. c m rightwards double arrow l cross times b equals 30 rightwards double arrow b equals 30 over l... left parenthesis 2 right parenthesis S u b s t i u t t i n g space t h e space v a l u e space o f space b space f r o m space e q u a t i o n space left parenthesis 2 right parenthesis space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma l plus 30 over l equals 12 rightwards double arrow fraction numerator l squared plus 30 over denominator l end fraction equals 12 rightwards double arrow l squared plus 30 equals 12 l rightwards double arrow l squared minus 12 l plus 30 equals 0 rightwards double arrow l squared minus 12 l plus 30 equals 0 rightwards double arrow l equals fraction numerator negative open parentheses negative 12 close parentheses plus-or-minus square root of open parentheses negative 12 close parentheses squared minus 4 cross times 30 end root over denominator 2 end fraction rightwards double arrow l equals fraction numerator 12 plus-or-minus square root of 144 minus 120 end root over denominator 2 end fraction rightwards double arrow l equals fraction numerator 12 plus-or-minus square root of 24 over denominator 2 end fraction rightwards double arrow l equals 6 plus-or-minus square root of 6 S i n c e comma space 6 plus-or-minus square root of 6 space i s space n o t space a n space i n t e g e r comma space n o space s u c h space r e c tan g l e space i s space p o s s i b l e space s a t i s f y i n g space t h e space g i v e n space c o n d i t i o n s. T h u s comma space n u m b e r space o f space r e c tan g l e s equals 0 K i n d l y space p o s t space o n e space q u e s t i o n space p e r space q u e r y.

Answered by Vimala Ramamurthy | 2nd Oct, 2015, 09:56: AM