Question

Ajay wants to stack few one-rupee coins and some five-rupee coins in such a way that: a. Each stack has the same number of coins. b. There is least number of stacks. c. Each stack either has one rupee or five-rupee coins. d. No coins are left over after creating stacks. His first step to find the number of coins that should be in each stack is 195=1(180) +15. Given that he has more of five-rupee coins than one-rupee coins, how many one-rupee coins stack can he make? *​

Answer 1

Given :- Ajay wants to stack few one-rupee coins and some five-rupee coins in such a way that :

a) Each stack has the same number of coins.

b) There is least number of stacks.

c) Each stack either has one rupee or five-rupee coins.

d) No coins are left over after creating stacks.

His first step to find the number of coins that should be in each stack is 195=1(180) +15. Given that he has more of five-rupee coins than one-rupee coins, how many one-rupee coins stack can he make ?

Solution :-

we have,

→ Number of coins in each step :- 195 = 1(180) + 15 .

since,

• Rs.5 coins > Rs.1 coine .
• 195 > 180 .

so,

→ Rs.5 coins = 195

→ Rs.1 coins = 180 .

now, in order to least number of coins in each stacks , we must find HCF of number of coins .

then,

→ 195 = 3 * 5 * 13

→ 180 = 2 * 2 * 3 * 3 * 5

→ HCF = 15 .

therefore,

→ Number of Rs.1 coins stacks = Total Rs.1 coins / HCF = 180/15 = 12 stacks (Ans.)

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