Q5 of 23 Page 1

Attempt of the following question:

A three-digit number is equal to 17 times the sum of its digits. If 198 is added to the number, the digits are interchanged. The addition of first and third digit is 1 less than middle digit. Find the number.

Let x,y,and z be the digits:


∴ the number becomes


⇒ 100x + 10y + z


⇒ 100x + 10y + z = 17(x + y + z)----a
⇒ 100x + 10y + z + 198 = 100z + 10y + x----b


100x + z + 198 = 100z + x


99x + 198 = 99z


x + 2 = z


Substitute in c


⇒ x + z + 1 = y----c
x + x + 2 + 1 = y
y = 2x + 3


⇒ Substitute both in a


100x + 10(2x + 3) + x + 2 = 17(x + 2x + 3 + x + 2)
100x + 20x + 30 + x + 2 = 68x + 85


53x + 32 = 85
53x = 53


x = 1,y = 5,z = 3


More from this chapter

All 23 →
4

Attempt of the following question:

Solve the following simultaneous equations:

4

Attempt of the following question:

In a certain race there are three boys A, B, C. The winning probability of A is twice than B and the winning probability of B is twice than C. If P(A) + P(B) + P(C) = 1, then find the probability of each boy.

 5

Attempt of the following question:

The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.

 5

Attempt of the following question:

Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.