Advertisements
Advertisements
Question
Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.
Advertisements
Solution
Let the unit’s digit be x.
Then, the ten’s digit = 11 – x
∴ Number = 10(11 – x) + x
= 110 – 10x + x
= 110 – 9x
Number obtained by interchanging the digits
= 10x + (11 – x)
= 9x + 11
According to the question,
9x + 11 – (110 – 9x) = 9
⇒ 9x + 11 – 110 + 9x = 9
⇒ 18x = 9 – 11 + 110
⇒ 18x = 108
⇒ x = `108/18`
⇒ x = 6
Hence, unit’s digit = 6 and ten’s digit = 11 – 6 = 5
Therefore, the required number is 56.
APPEARS IN
RELATED QUESTIONS
Amina thinks of a number and subtracts `5/2` from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?
A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?
One of the two digits of a two digit number is three times the other digit. If you interchange the digit of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?
Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of this mother’s present age. What are their present ages?
There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate Rs 100 per metre it will cost the village panchayat Rs 75, 000 to fence the plot. What are the dimensions of the plot?
Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him Rs 50 per metre and trouser material that costs him Rs 90 per metre. For every 2 meters of the trouser material he buys 3 metres of the shirt material. He sells the materials at 12% and 10% profit respectively. His total sale is Rs 36660. How much trouser material did he buy?
Arjun is twice as old as Shriya. Five years ago his age was three times Shriya’s age. Find their present ages.
A and B are together 90 years old. Five years ago A was thrice as old as B was. Hence, the ages of A and B five years back would be (x – 5) years and (85 – x) years respectively.
In a two-digit number, digit in units place is twice the digit in tens place. If 27 is added to it, digits are reversed. Find the number.
