CBSE Class 10 Answered

<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"><ol> <li style="font-size: 12.000000pt; font-family: 'CMR12';"> <p><span style="font-size: 12pt;">When the positive integers </span><span style="font-size: 12.000000pt; font-family: 'CMMI12';">a, b </span><span style="font-size: 12pt;">and </span><span style="font-size: 12.000000pt; font-family: 'CMMI12';">c </span><span style="font-size: 12pt;">are divided by 13, the respective remainders are 9, 7 </span><span style="font-size: 12pt;">and 10. When </span><span style="font-size: 12pt; font-family: CMMI12;">a </span><span style="font-size: 12pt;">+ 2</span><span style="font-size: 12pt; font-family: CMMI12;">b </span><span style="font-size: 12pt;">+ 3</span><span style="font-size: 12pt; font-family: CMMI12;">c </span><span style="font-size: 12pt;">is divided by 13, what is the remainder </span></p> </li> </ol></div> </div> </div>

Asked by priyankajaju | 28 Jul, 2016, 06:26: PM

Expert Answer

begin mathsize 20px style G i v e n space t h r e e space n u m b e r s space a r e space a space comma b space a n d space c. N o w space a s space g i v e n space w h e n space t h e s e space a r e space d i v i d e d space b y space 13 space t h e y space g i v e space r e m a i n d e r space 9 comma 7 space a n d space 10 space r e s p e c t i v e l y. T h e r e f o r e space b y space E u c l i d space D i v i s i o n space L e m m a space f o r space p o s i t i v e space n u m b e r s space a comma b space a n d space c space t h e r e space e x i s t space u n i q u e space i n t e g e r s x space comma y space a n d space z space s u c h space t h a t colon a equals 13 x plus 9 b equals 13 y plus 7 c equals 13 z plus 10 n o w space f i n d i n g space t h e space v a l u e space o f space a plus 2 b plus 3 c space g i v e s space a plus 2 b plus 3 c equals 13 x plus 9 plus 26 y plus 14 plus 39 z plus 30 a plus 2 b plus 3 c equals 13 x plus 26 y plus 39 z plus 53 W h e n space d i v i d e d space b y space 13 space g i v e s space r e m a i n d e r space a s space 1 A s space w e space c a n space s e e space t h a t space 13 x space 26 y space a n d space 39 z space a r e space d i v i s i b l e space b y space 13 space l e a v i n g space n o space r e m a i n d e r space a s space t h e y space a r e space m u l t i p l e space o f space 13 space i t s e l f b u t space w h e n space 53 space i s space d i v i d e d space b y space 13 space i t space g i v e s space 1 space a s space r e m a i n d e r h e n c e comma space a plus 2 b plus 3 c space d i v i d e d space b y space 13 space g i v e s space 1 space a s space r e m a i n d e r. space end style

Answered by Vijaykumar Wani | 29 Jul, 2016, 11:53: AM

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