Question

A man has an equal number of ₹2 and ₹5 coins. He has also some ₹1 coins. If the total number of coins is 40 and their value is ₹ 120, how many ₹5 and ₹2 coins does he have ?

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Answer 1

Answer:

ʟᴇᴛ ᴛʜᴇ ᴛᴏᴛᴀʟ ɴᴜᴍʙᴇʀ ᴏғ ᴄᴏɪɴs ʙᴇ 12x.

ᴛʜᴇɴ,

ɴᴜᴍʙᴇʀ ᴏғ ʀs.5 ᴄᴏɪɴs = 3x

ɴᴜᴍʙᴇʀ ᴏғ ʀs.2 ᴄᴏɪɴs = 4x

ɴᴜᴍʙᴇʀ ᴏғ ʀᴇ.1 ᴄᴏɪɴs = 5x

ᴛᴏᴛᴀʟ ᴠᴀʟᴜᴇ ᴏғ :-

ʀs.5 ᴄᴏɪɴs = 3x * 5 = 15x

ʀs.2 ᴄᴏɪɴs = 4x * 2 = 8x

ʀᴇ.1 ᴄᴏɪɴs = 5x * 1 = 5x

ɢɪᴠᴇɴ, ᴛᴏᴛᴀʟ ᴠᴀʟᴜᴇ ᴏғ ᴀʟʟ ᴄᴏɪɴs = 224

ᴛʜᴇʀᴇғᴏʀᴇ,

15x + 8x + 5x = 224

28x = 224

x = 8

ᴛᴏᴛᴀʟ ɴᴜᴍʙᴇʀ ᴏғ ᴄᴏɪɴs = 12x = 12 * 8 = 96

ɴᴜᴍʙᴇʀ ᴏғ,

ʀs.5 ᴄᴏɪɴs = (3/12) * 96 = 24 ᴄᴏɪɴs

ʀs.2 ᴄᴏɪɴs = (4/12) * 96 = 32 ᴄᴏɪɴs

ʀᴇ.1 ᴄᴏɪɴs = (5/12) * 96 = 40 ᴄᴏɪɴs

(ɢɪᴠᴇɴ ɴᴏ. ᴏғ ʀs.5, ʀs.2, ᴀɴᴅ ʀᴇ.1 ᴄᴏɪɴs ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ ᴏғ 3:4:5)

ғɪɴᴀʟ ᴀɴsᴡᴇʀ : ᴛʜᴇ ʙᴏʏ ʜᴀs 40 ʀᴇ.1 ᴄᴏɪɴs.

ʟᴇᴛ's ᴄʀᴏss ᴠᴇʀɪғʏ ᴛʜᴇ ᴀɴsᴡᴇʀ ᴏɴᴄᴇ.

(24*5) + (32*2) + (40*1)

= 120 + 64 + 40

= 224 = ᴠᴀʟᴜᴇ ɢɪᴠᴇɴ ɪɴ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ.