Question

by selling 70 pencile for Rs 90/- a person makes a loss of 25%. How many pencile should be sold for Rs 234 to have profit of 30%.​

Answer 1

Answer:

To sell the pens for Rs 234 and make a 30 % profit. then we need to sell 105 pens approximately.

Step-by-step explanation:

Required formulas:

CP = \frac{100}{100+- (G or L)} * S.P.

S.P. = \frac{100 +- (G or L)}{100} * C.P.

Step 1:

The S.P of 70 pens = Rs. 90

Loss % = 25%

∴ C.P. of 70 pens = \frac{100}{100 - 25} * 90 = \frac{100}{75} * 90 = Rs. 120

Now, C.P. of 1 pen = \frac{120}{70} = Rs. 1.71

Step 2:

Here we want to have a profit of 30%

∴ S.P. of 1 pen = \frac{100 + 30}{100} * 1.71 = \frac{130}{100} * 1.71 = Rs. 2.22

So, we can say that

When the S.P. is Rs. 2.22, we can sell 1 pen at 30% profit

∴ When S.P. is Rs. 234, we can sell = \frac{1}{2.22} * 234 = 105.40 ≈ 105 pens at 30% profit.

Thus, we need to sell 105 pens for Rs. 234 to make a profit of 30%.

Step-by-step explanation:

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Answer 2

GIVEN :

• NUMBER OF PENCILS SOLD FOR Rs.90 IS 70 AND LOSS INCURRED IS 25%

TO FIND :

• NUMBER OF PENCILS THAT SHOULD BE SOLD FOR Rs.234 TO MAKE A PROFIT OF 30%

SOLUTION :

SELLING PRICE (SP) OF 70 PENCILS = Rs.90

LOSS% = 25%

LET COST PRICE OF 70 PENS BE (CP)

$loss\% = \frac{(cp - sp) \times 100}{cp} \\ \\ = > 25 = \frac{(cp - 90) \times 100}{cp} \\ \\ = > 25cp = (cp - 90) \times 100 \\ \\ = > 25cp = 100cp - 9000 \\ \\ = > 75cp = 9000 \\ \\ = > cp = rs.120$

WE HAVE GOT THAT COST PRICE (CP) OF 70 PENCILS IS Rs.120

THEN COST PRICE OF 1 PENCIL = 120/70 = Rs. 1.71

LET THE NUMBER OF PENCILS THAT SHOULD BE SOLD BE 'n'

THEN COST PRICE (CP)' OF 'n' PENCILS = n × CP OF ONE PENCIL = n × 1.71 = Rs.1.71 n

GIVEN THAT SELLING PRICE (SP)' OF 'n' PENCILS = Rs.234

PROFIT % = 30%

$= > \frac{(sp - cp) \times 100}{cp} = 30 \\ \\ = > \frac{(234 - 1.71n) \times 100}{1.71n} = 30 \\ \\ = > 23400 - 171n = 51.3n \\ \\ = > 23400 = 222.3n \\ \\ = > n = 105$

VERIFICATION :

IF NUMBER OF PENCILS THAT SHOULD BE SOLD AT Rs.234 TO GAIN 30% BE 105

THEN (CP)' OF 105 PENCILS = 1.71 × 105 = Rs.179.55

$profit\% = 30\% \\ \\ = > 30 = \frac{(sp - cp) \times 100}{cp} \\ \\ = > 30 = \frac{(234 - 179.55) \times 100}{179.55} \\ \\ = > 30 = \frac{(54.45) \times 100}{179.55} \\ \\ = > 30 = \frac{5445}{179.55} \\ \\ = > 30 = 30$

∴ THE NUMBER OF PENS THAT MUST BE SOLD TO GAIN 30% AT THE RATE Rs. 234 IS 105

FORMULA USED :

$i) \: profit\% = \frac{(sp - cp) \times 100}{cp}$