Question

12. bhaskar buys an estate for 34 lakh. He builds e boundary wall around it at a cost of 2 lakh He cells two-fifths ofitat a loss of 20% and one-third of cat a gain of 25%. At what gain per cent must he sell the remainder, so as to make a profit of 5% on the whole?​

Answer 1

❏Given:-

• Bhaskar buys an estate for 34 lakhs
• He built a boundary wall around it at the cost of 2 lakhs
• He sold two-fifth of it at the loss of 20% and one-third of it at a gain of 25%

❏To Find:-

• The gain percent at which he will sell the remainder of the estate, so as to make a profit of 5% whole

❏Solution:-

Total cost of the estate:- ₹34,00,000 + ₹2,00,000

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ= ₹3,600,000

CP of 2/5th of the estate:- ${ \large \sf \frac{2}{5}} \sf\small\times 3600000$

$\qquad\qquad\quad : \longmapsto { \large \sf \frac{2}{ \cancel{5}} {\sf\small\times \cancel{3600000}} = \small RS~ 14400000}$

Now,

Given loss% = 20%

Hence SP of 2/5th of the estate:-

$\boxed{ \frak {\orange{Formula~used = \frac{100 - loss (Percent)}{100} \times CP }}}$

$: \longmapsto{ \large \frac{100 - 20}{100} \small\times 14400000}$

$: \longmapsto{ \large \sf \frac{100 - 20}{1 {\cancel{00} }} \small\times 144000 {\cancel {00}}}$

$: \longmapsto \sf {80} \times 144000 = RS~152000$

Now,

CP of 1/3rd of the estate:-

$\sf : {\large \longmapsto \frac{1}{3}} \small \times 3600000$

$: \longmapsto { \large \sf \frac{1}{ \cancel{3}} {\sf\small\times \cancel{3600000}} = \small RS~1200000}$

Given Gain% = 25%

SP of 1/3rd of the estate=

$\boxed{ \frak {\green{Formula~used = \frac{100 - gain(percent)}{100} \times CP }}}$

$: \longmapsto{ \large \frac{100 - 25}{100} \small\times 1200000}$

$: \longmapsto{ \large \sf \frac{100 - 25}{1 {\cancel{00} }} \small\times 12000 {\cancel {00}}}$

$: \longmapsto \sf {125} \times 12000 = RS~1500000$

∴The remaining part:-

➺ 3600000 – (1400000 + 1200000)

➺ 3600000 – 2640000

➺ ₹960000

Now, Finding the SP of the whole estate to make a profit of 5% :-

$\sf : \longmapsto 3600000 +{ \large \frac{5}{100} \small\times 3600000}$

$: \longmapsto{ \large \sf \frac{5}{1 {\cancel{00} }} \small\times 36000 {\cancel {00}}}$

$\sf : \longmapsto 3600000 + 5 \times 3600 = 3600000 + 18000$

$\sf : \longmapsto RS~3780000$

SP of the remainder of amount =

➺ 3780000 – 150000 – 1152000

➺ ₹112800000

Now, Profit:-

SP - CP

➺ 11280000 - 960000

➺ ₹1680000

Profit%:-

$:\longmapsto\sf\large\frac{Profit}{CP}$

$:\longmapsto\sf\large\frac{1680000}{960000}\small\times 100$

$: \longmapsto{ \large \sf \frac{1680{\cancel{00}}}{96 {\cancel{0000}}} \small\times 1 {\cancel {00}}}$

= 17·5% Answer

$\rule{200pt}{3pt}$