At a certain stationery shop, the cost of each ruler is
2.5 times the cost of each sharpener. Anil bought
25 rulers and a certain number of sharpeners. Had he
bought as many rulers as the number of sharpeners that he bought and vice versa, his total expenditure on the two items would have been 9. % less. How
many sharpeners did he buy
Answers
Given : the cost of each ruler is 2.5 times the cost of each sharpener.
Anil bought 25 rulers and a certain number of sharpeners.
As he bought as many rulers as the number of sharpeners that he bought and vice versa his total expenditure on the two items would have been ≈ 9. % les
To Find : How many sharpeners did he buy
Solution:
cost of each sharpener. = C
cost of each ruler = 2.5C
Anil bought 25 rulers and S sharpeners
Total Cost = 25 * 2.5C + SC
= 62.5C + SC
= C (S + 62.5)
Anil bought S rulers and 25 sharpeners
Total Cost = 25 *C + S(2.5C)
= 2.5C( S + 10)
C (S + 62.5) ( 1 - 9/100) = 2.5C( S + 10)
=> (S + 62.5) ( 91/100) = 2.5( S + 10)
=> 91S + 5,687.5 = 250S + 2500
=> 3,187.5 = 159S
=> S = 20.04
S ≈ 20
20 Sharpeners
Verification
25 * 2.5C + 20C = 82.5C
20*2.5C + 25C = 75C
((82.5C - 75C)/82.5C)*100 = 9.09 % ≈ 9 %
20 Sharpeners he bought
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