Question

Arjun spent Rs.12 to purchase some pens and pencils.The cost of a pen and pencil are in the ratio 3:2.
the total cost of a pen and a pencil is Rs. 3.
if the total number of pens and pencils he purchased is7,
find the number of pens he purchased.

Answer 1

let the cost of a pen be 3x
let the cost of a pencil be 2x , ( notice 3x : 2x = 3:2 )

number of pens --- a
number of pencils --- 7-a , because their sum is 7

3x + 2x = 3
5x = 3
x = Rs 3/5 = Rs 0.6

so a pen costs Rs 1.8
and a penci costs Rs 1.2

1.8a + 1.2(7-a) = 12
1.8a + 8.4 - 1.2a = 12
.6a = 3.6
a = 6

so there were 6 pens purchased and 1 pencil

check:
1+6 = 7 , number of pens and pencils checks!
cost of pen = 1.8
cost of pencil = 1.2
ratio is 1.8 : 1.2 = 3 : 2 , ratio costs checks!

6pens + 1 pencil = 6(1.8) + 1.2 = 12

All looks good!

Answer 2

nice clear explanation