Permutation-Combination
Aptitude

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Q.

Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos?

 A.

16

 B.

17

 C.

18

 D.

19

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Solution:
Option(C) is correct

Let the number of currency 1 Miso, 10 Misos and 50 Misos be $x, y$ and $z$ respectively.

$x + 10y + 50z = 107$

Now the possible values of $z$ could be 0, 1 and 2.

For, $z = 0$: $x + 10y = 107$

Number of integral pairs of values of $x$ and $y$ that satisfy the equation:

$x + 10y = 107$ will be 11.

These values of $x$ and $y$ in that order are:

$(7, 10); (17, 9); (27, 8)…(107, 0)$

For $z = 1$: $x + 10y = 57$

Number of integral pairs of values of $x$ and $y$ that satisfy the equation:

$x + 10y = 57$ will be 6.

These values of $x$ and $y$ in that order are:

$(7, 5); (17, 4); (27,3); (37, 2); (47, 1) \text{ and } (57, 0)$

For $z = 2$: $x + 10y = 7$

There is only one integer value of $x$ and $y$ that satisfies the equation:

$x + 10y = 7$ in that order is $(7, 0)$

Therefore total number of ways in which you can pay a bill of 107 Misos:

$= 11 + 6 + 1$

$= \textbf{18}$


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