1/17 th of the cost price is 1/22 of S.P. 10% of the C.P. and 5% of the S.P. differ by 12. Find the C.P. and S.P.
Answers
Step-by-step explanation:
Given:-
1/17 th of the cost price is 1/22 of S.P. 10% of the C.P. and 5% of the S.P. differ by 12.
To find:-
Find the C.P. and S.P. ?
Solution:-
1/17 th of the cost price is 1/22 of S.P
=>(1/17)× CP = (1/22) × SP
=>CP = (1/22)×SP × (17/1)
=>CP = (17/22) × SP
Therefore, CP = (17 /22) SP ----------(1)
10% of the C.P.
=>10% × CP
=>(10/100) × CP
=>(1/10)× CP
=>CP/10
5% of the SP
=>5% × SP
=>(5/100)×SP
=>(1/20)× SP
=>SP/20
10% of the C.P. and 5% of the S.P. differ by 12.
=>(CP/10)-(SP/20) = 12
=>(2CP-SP)/20 = 12
=>2CP -SP = 12×20
=>2CP - SP = 240
=>2(17/22)SP -SP = 240. (from (1))
=>(34/22)SP-SP = 240
=>(17/11)SP -SP = 240
=>(17SP -11SP)/11 = 240
=>6SP /11 = 240
=>6SP = 240×11
=>6SP = 2640
=>SP = 2640/6
=>SP = 440
Selling Price = Rs. 440
On Substituting the value of SP in (1)
CP = (17 /22) SP
=>CP = (17/22)×440
=>CP = (17×440)/22
=>CP = 17×20
=>CP = 340
Cost Price = Rs. 340
Answer:-
Cost Price = Rs. 340
Selling Price = Rs. 440
Check:-
1/17th of CP
=>(1/17)×340
=>340/17
=>20
1/22 of SP
=>(1/22)×440
=>440/22
=>20
1/17th of CP = 1/22nd of SP
10% of CP
=>(10/100)×340
=>3400/100
=>34
5% of SP
=>(5/100)×440
=>5×440/100
=>2200/100
=>22
10% of the C.P. - 5% of the S.P
=>34-22
=>12
Verified the given relations