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प्रश्न
A certain number of eggs are bought at 4 for 5 and an equal number at 9 for Rs.10. If 15% were broken in transaction and remaining were sold at 2 for Rs.3, find the profit percent and the number of eggs of each kind bought, if Rs.510 were gained on the whole.
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उत्तर
Let the number of eggs bought at 4 for Rs.5 be x.
∴ The number of eggs bought at 9 for Rs.10 are x
∴ Total number of eggs bought = x + x = 2x
When eggs are bought at 4 for Rs.5, C.P. of each egg = Rs.`(5)/(4)`
C.P. of x eggs = `"Rs."(5)/(4)x`
When eggs are bought at 9 for Rs.10, C.P. of each egg =Rs.`(10)/(9)`
C.P. of x eggs = `"Rs."(10)/(9)x`
∴ Total C.P.
= `"Rs."(5)/(4)x + "Rs."(10)/(9)x`
= `"Rs."(85)/(36)x`
Number of eggs broken = 15% of 2x
= `(15)/(100) xx 2 x`
= `(3x)/(10)`
Eggs left
= `2x - (3x)/(10)`
= `(17x)/(10)`
When eggs are sold at 2 for Rs.3, S.P. of each egg = `"Rs."(3)/(2)`
S.P. of `(17)/(10) xx "eggs"`
= `"Rs."(3)/(2) xx (17)/(10) xx = "Rs."(51)/(20)xx`
Gain = S.P. - C.P.
= `(51)/(20) x - (85)/(36) x`
= `((459 - 425)/(180))x`
= `(34)/(180)x`
= `"Rs."(17)/(90)x`
Gain % = `"gain"/"C.P." xx 100`
= `(17/90x)/(85/36x) xx 100`
= `(17)/(90) xx (36)/(85) xx 100`
= 8%
Also, gain = Rs.510
⇒ `(17)/(90)x` = 510
⇒ x = `(90)/(17) xx 510`
= 2700
∴ Number of eggs of each kind bought = 2700.
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