Question 15 - CBSE Class 10 Sample Paper for 2018 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

Seven times a two digit number is equal to four times the number obtained by reversing the order of its digits. If the difference of the digits is 3, determine the number.

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

Question 15
Seven times a two digit number is equal to four times the number obtained by reversing the order of its digits. If the difference of the digits is 3, determine the number.
Number is of the form
Let digit at units place = y
and the digit at tens place = x
Number = 10x + y
Reversed Number = 10y + x
Given that
7 times number is equal to 4 times reverse of number
7 (Number) = 4 (Reversed Number)
7 (10x + y) = 4 (10y + x)
70x + 7y = 40y + 4x
70x 4x = 40y 7y
66x = 33y
x = 33 /66
x = /2
Also,
given that
Difference of digits is 3
So x y = 3
or
y x = 3
Since x = /2
x is smaller than y
So, x y will be negative ( /2 =( )/2)
We can t use x y = 3
Thus, our equations are
x = /2 (1)
y x = 3 (2)
From (2)
y x = 3
Putting x = /2
y /2 = 3
/2 = 3
y = 3 2
y = 6
Putting y = 6 in (1)
x = /2
x = 6/2
x = 3
Hence x = 3, y = 6 is the solution
Number = 10x + y = 10(3) + 6 = 30 + 6 = 36
Number = 36

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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