Question

Srishti bought two hens for Rs. 1300. She sold one at a loss of 5% and the other at a gain of 8%. What will be the cost price of each hen respectively if she faced neither loss nor gain in this transaction?

Answer 1

Answer:

she is getting loss of Rs.32.5 on first hen. and Rs.52 profit on second hen.

on first hen she should sell on Rs.682.5 .

and on second hen she should sell it of Rs.592.

so the cost price of both the hen is 1274.5

Answer 2

SOLUTION:-

════════════

Given:

Shrishti bought two hens for Rs.1300.She sold one at a loss of 5% & other at a gain of 8%.

To find:

══════

The cost price of each hen respectively, i she faced neither loss nor gain in this transaction.

Explanation:

═════════

•Let the cost price [C.P.] of first hen be Rs.R

•Let the cost Price [C.P.] of second hen be Rs. M.

According to the question:

═════════════════

R + M= 1300

=) M= 1300 - R..................(1)

Using Formula:

══════════

Selling price= [(100 - loss%)/100] × C.P

Selling price= [(100+ gain%)/100]× C.P

Therefore,

1st hen was sold at 5% loss;

$S.P. = [\frac{(100 - loss\%)}{100}] \times C.P. \\ \\ S.P. = [\frac{(100 - 5\%)}{100} ]\times R \\ \\ S.P. = ( \frac{95R}{100} ) \\ \\ S.P. =Rs.0.95R$

&

In 2nd hen was sold at 8% gain;

$S.P. = [\frac{(100 + gain\%)}{100} ] \times C.P. \\ \\ S.P. = [ \frac{(100 + 8\%)}{100} ] \times M \\ \\ S.P. = ( \frac{108M}{100} ) \\ \\ S.P . = Rs.1.08M$

Therefore,

Neither profit nor loss was incurred in the entire transaction, overall selling price be equal to cost price.

We have,

=) 0.95R + 1.08M= 1300.............(2)

Substituting the value of equation (1) & equation (2), we get;

Putting the value of M in equation (2),

=) 0.95R + 1.08(1300-R)= 1300

=) 0.95R + 1404 - 1.08R= 1300

=) 0.95R - 1.08R = 1300 - 1404

=) - 0.13R = -104

=) R= 104/0.13

$= > R = \frac{104 \times 100}{0.13 \times 100} \\ \\ = > R = \frac{10400}{13} \\ \\ = > R = Rs.800...............(3)$

Putting the value of R in equation (1), we get;

=) M= Rs.[1300 - 800]

=) M= Rs.500

:)