# DILR-1

The currency of the country Banama is Rupas (Rp). There are exactly five
denominations in which the currency is available – Rp 2, Rp 3, Rp 7, Rp 17 and Rp
19.
Each of five persons, A through E, had notes of exactly one denomination with him
and no two persons among the five had notes of the same denomination. On a
particular day, the five persons visited a shop and each of them purchased a
different product. The amounts that A through E paid the shopkeeper were Rp 102,
Rp 357, Rp 399, Rp 238 and Rp 147, in that order. Further, the number of notes
that each person gave the shopkeeper was distinct. However, the amount that
each person paid the shopkeeper was more than the price of the product that he
purchased. Therefore, the shopkeeper returned the excess amounts to each of A
through E in the form of 2 notes, 4 notes, 1 note, 2 notes and 1 note respectively,
but in denomination(s) different from that in which the person had paid the
shopkeeper.

Q1)What is the total number of notes that the five persons paid the shopkeeper?


Q2)Which of the following cannot be the price (in Rp) of the product that A purchased?
a) 76
b) 92
c) 80
d) 82


Q3)How many of the following statements are definitely true?
I. The price of the product that A purchased is an even number.
II. The price of the product that B purchased is an even number.
III. The price of the product that C purchased is an odd number.
IV. The price of the product that D purchased is an even number.
a) 0
b) 1
c) 2
d) 3


Q4)Which of the following statements is sufficient to determine the price of the product that E purchased?
a) The price of the product is not a multiple of 10.
b) The price of the product is a multiple of 10.
c) The price of the product is not a multiple of 5.
d) None of the above

SOLUTION-

 We know the amount paid by each person,
A=102
B=357
C=399
D=238
E=147

Denomination available in country= 2,3,7,17 and 19

Further, it is given that each person has only one type of denomination.
Now how to proceed further?
The problem can be solved by factorising the amount paid by each person but why to factorise is the main question?

Taking A into consideration,
A paid 102 = 2*3*17
Now if A has only RS.2 denomination he must have 51 notes of it.
Similarly, if A has RS.3 denomination he must have 34 notes of it.
and if having Rs.17 denomination then 6 notes will be there.

Now,
A=102 = 2*3*17
B=357 =3*7*17
C=399 =3*7*19
D=238 =2*7*17
E=147 =3*7*7

Now, we definitely know the denomination with C i.e; 19 and the total number he has is 21.
Further, we can see only 2 payments are even,i.e,A and D so either A has 2 as its denomination or D has 2 as its denomination.

Now, just make cases,

A can have 51,34 or 6 notes in the denomination of 2,3 or 17 respectively.
B can have 119 or 51 notes in the denomination of  3 or 7 respectively. B cannot have 17 as its denomination because C already has 21 notes.
D can have 119,34 or 14 notes in the denomination of 2,7 or 17 respectively.
E will have 3 as its denomination with total 49 notes otherwise it will have 21 notes if 7 is taken as its denomination.

Now, we are down to 3 persons, A, B and D.
Now, B is only left Rs.7 denomination as E already has Rs.3 as its denomination.
So, B has 51 notes with Rs.7 denomination with him.
Now, A is left with 2 or 17 as its denomination.If A's denomination is Rs.2 then A will have 51 notes which are not possible as B already has 51 notes with him. So, A will have Rs.17 as its denomination.

Deducing Further,
A=Rs.17 (6)-returned -2
B=Rs.7(51)-returned-4
C=Rs.19(21)-returned-1
D=Rs.2(119)-returned-2
E=Rs.3(49)-returned-1

Now, solving questions will be a cakwalk.

Q1)What is the total number of notes that the five persons paid the shopkeeper?

SUM=6+51+21+119+49=246 ANS

Q2)Which of the following cannot be the price (in Rp) of the product that A purchased?
a) 76
b) 92
c) 80
d) 82

A has paid Rs.102 with 17 as denomination and is returned 2 notes that can be anyone of 2,3,7 and 19 or their combinations.
102 = 76+19+7
102 = 92+7+7
102 = 80+3+19
102 = 82+20- not possible
Q3)How many of the following statements are definitely true?
I. The price of the product that A purchased is an even number.
II. The price of the product that B purchased is an even number.
III. The price of the product that C purchased is an odd number.
IV. The price of the product that D purchased is an even number.
a) 0
b) 1
c) 2
d) 3
In such questions instead of proving the question, correct try to prove it wrong.
A=102-2-3=97-hence product cost could be odd.
B=357-2-2-2-2=349 = odd
C=399-7=even
D=238-odd-odd(as it has 2 as its denomination)- DEFINITELY TRUE.
So, only 1 statement is definitely true among the 4 given statements.
Hence, option (b) is the ANS.

Q4)Which of the following statements is sufficient to determine the price of the product that E purchased?
a) The price of the product is not a multiple of 10.
b) The price of the product is a multiple of 10.
c) The price of the product is not a multiple of 5.
d) None of the above

E=3(49)=147 with 1 note returned.
For option (a),returned note can be 2 or 19 not possible.Hence,eliminated.
For option (b), returned note can be 7 or 17 so not possible.Hence, eliminated.
For option (c), returned note has to be 19. Hence it is the answer.