Q2 of 40 Page 92

The sum of a two digit number and the number obtained reversing the digits is 66. If the digits of the number differ by 2, find the number. how many such numbers are there?

Let the digit in the unit’s place be x and the digit in the tens place be y.

Then, the number = 10y + x


The number obtained by reversing the order of the digits = 10x + y


According to given conditions,


(10y + x) + (10x + y) = 66


⇒ 11(x + y) = 66


⇒ (x + y) = 6


According to second situation, digits differ by 2


So, either x – y = 2 or y – x = 2


Thus , we have the following sets of simuntaneous equations


x + y = 6 …I


x – y = 2 …II


or,


x + y = 6 …III


x – y = 2 …IV


solving equation I and II, we get x = 2 and y = 4


solving equation III and IV , we get x = 4 and y = 2


When x = 4 and y = 2,


Two digit number = (10y + x) = 10(4) + 2 = 42


When x = 2 and y = 4,


Two digit number = (10y + x) = 10(2) + 4 = 24


Hence, the required number is either 24 or 42.


More from this chapter

All 40 →
9

In X class, if three students sit on each bench, one student will be left. If four students sit on each bench, one bench will be left. Find the number of students and the number of benches in that class.

 1

The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save D2000 per month, find their monthly income.

 3

The larger of two supplementary angles exceeds the smaller by 18o. Find the angles.

 4

The taxi charges in Hyderabad are fixed, along with the charge for the distance covered. For a distance of 10 km., the charge paid is D220. For a journey of 15km. the charge paid is D310.

i. What are the fixed charges and charge per km?


ii. How much does a person have to pay for travelling a distance of 25 km?