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ICSE Class 10 Answered

A twodigits number contains the smaller of the two digits in the unit place . The product of the digits is 40 and the difference between the digits is 3. Find the number.
Asked by maitripatel9069.10sdatl | 16 Apr, 2020, 10:52: AM
answered-by-expert Expert Answer
Let a be the smaller of the two digits, so it must be at the unit's place and b be the digit at ten's place.
The number is 10b + a.
According to the first condition,
a cross times b equals 40 space... space left parenthesis i right parenthesis A c c o r d i n g space t o space t h e space s e c o n d space c o n d i t i o n comma b minus a equals 3 rightwards double arrow b equals 3 plus a space space... space left parenthesis i i right parenthesis S u b s t i t u t i n g space b space f r o m space left parenthesis i i right parenthesis space i n space left parenthesis i right parenthesis comma space w e space g e t a open parentheses 3 plus a close parentheses equals 40 rightwards double arrow a squared plus 3 a minus 40 equals 0 rightwards double arrow a squared plus 8 a minus 5 a minus 40 equals 0 rightwards double arrow a left parenthesis a plus 8 right parenthesis minus 5 left parenthesis a plus 8 right parenthesis equals 0 rightwards double arrow left parenthesis a plus 8 right parenthesis left parenthesis a minus 5 right parenthesis equals 0 rightwards double arrow a equals negative 8 space space o r space space a equals 5 a space c a n apostrophe t space b e space n e g a t i v e rightwards double arrow a equals 5 rightwards double arrow b equals 8 H e n c e comma space t h e space r e q u i r e d space n u m b e r space i s space 85.
Answered by Renu Varma | 17 Apr, 2020, 10:51: AM

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