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The sum of two natural numbers is 17402. One of the two numbers is divisible by 10. If the units digit of that number is erased, the other number is obtained. What is the difference of these two numbers?

a) 10,272
b) 11,700
c) 13, 362
d) 14, 238
e) 15426

Answer :

Sqdancefango

9514 1404 393

Answer:

  d)  14,238

Step-by-step explanation:

Suppose the smaller number is n. If the larger number gives the smaller when it is divided by 10, then the larger number is 10n. The sum of the two numbers is ...

  n + 10n = 11n = 17402  ⇒  n = 17402/11

The difference of the two numbers is ...

  10n -n = 9n = (9)(17402/11)

This means the difference of the two numbers is 9/11 of the sum, so is ...

  (9/11)(17402) = 14,238 . . . . matches D

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