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A two-digit number is 4 times the sum of its digits. If the digits are reversed, the new number is 18 more than the original. What is the number?

A24

B30

C36

D32

Answer:

A. 24

Read Explanation:

Let the two-digit number be (10a+b), where:

  • (a) = tens digit

  • (b) = units digit

Step 1: Use the first condition

The number is 4 times the sum of its digits:

10a+b = 4(a+b)

10a+b = 4a+4b
6a = 3b
b = 2a

Step 2: Use the second condition

When the digits are reversed, the new number is 18 more than the original:

10b+a = (10a+b)+18
9b-9a = 18
b-a = 2

Substitute (b=2a):

2a-a = 2
a = 2

Therefore,

b = 4

Step 3: Find the number

10a+b = 10(2)+4 = 24

The number is 24


Related Questions:

What will come in the place of the question mark (?) in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged? 15 − 5 + 18 × 6 ÷ 3 = ?
What will come in the place of the question mark (?) in the following equation if ‘+’ and ‘÷’ are interchanged and ‘−’ and ‘×’ are interchanged? 11÷ 9 + 3 − 6 × 8 = ?

Select the set in which the numbers are related in the same way as the following sets.

(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers info its

constituent digits. E.g. 13 — Operations on 13 such as adding /deleting/multiplying etc. to 13 can be performed.

Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)

(12,15,18)

(45,35,25)

What will come in the place of the question mark (?) in the following equation if '+' and '-' are interchanged and 'x' and '÷' are interchanged? 90 - 6 + 69 ÷ 54 × 27 = ?
- എന്നാൽ ÷ എന്നും, + എന്നാൽ × എന്നും, ÷ എന്നാൽ - എന്നും , × എന്നാൽ '+' എന്നുമായാൽ താഴെ തന്നിട്ടുള്ളവയിൽ ശരിയായ പ്രസ്താവന ഏത്?