बाय सेलिंग न टाइप ऑफ रूपीस 252 शॉपकीपर गेम्स 5% अट व्हाट प्राइस शोल्ड ई सेल द काइट गेम 30%
Answers
Answer:
Given
\begin{gathered} \to \sf \int \dfrac{9 {r}^{2} }{ \sqrt{1 - {r}^{3} } } dr \\ \end{gathered}
→∫
1−r
3
9r
2
dr
Using Substitution Method ,Let
\to \sf \: 1 - {r}^{3} = u→1−r
3
=u
Now Differentiate on both side wrt r
\sf \to \dfrac{d(1 - {r}^{3} )}{dr} = \dfrac{du}{dr}→
dr
d(1−r
3
)
=
dr
du
\sf \to \: - 3 {r}^{3 - 1} = \dfrac{du}{dr}→−3r
3−1
=
dr
du
\sf \to \: - 3 {r}^{2} = \dfrac{du}{dr}→−3r
2
=
dr
du
\sf \to \: (3 {r}^{2} )dr = - du→(3r
2
)dr=−du
Now we can write as
\begin{gathered} \to \sf3 \int \dfrac{3 {r}^{2} }{ \sqrt{1 - {r}^{3} } } dr \\ \end{gathered}
→3∫
1−r
3
3r
2
dr
Put the value
\begin{gathered} \sf \to \: 3\int \dfrac{ - du}{ \sqrt{u} } \\ \end{gathered}
→3∫
u
−du
\begin{gathered} \sf \to \: - 3\int \dfrac{ du}{ \sqrt{u} } \\ \end{gathered}
→−3∫
u
du
\begin{gathered}\sf \to \: - 3\int \dfrac{ du}{ {u} {}^{ \frac{1}{2} } } \\ \end{gathered}
→−3∫
u
2
1
du
\begin{gathered} \sf \to \: - 3 \int ({u}^{ \frac{ - 1}{2} } )du \\ \end{gathered}
→−3∫(u
2
−1
)du
\sf \to \: - 3 \bigg( \dfrac{u {}^{ \frac{ - 1}{2} + 1 } }{ \dfrac{ - 1}{2} + 1} \bigg) + c→−3(
2
−1
+1
u
2
−1
+1
)+c
\sf \to \: - 3 \bigg( \dfrac{ {u}^{ \frac{ - 1 + 2}{2} } }{ \dfrac{ - 1 + 2}{2} } \bigg) + c→−3(
2
−1+2
u
2
−1+2
)+c
\sf \to - 3 \bigg( \dfrac{u {}^{ \frac{1}{2} } }{ \dfrac{1}{2} } \bigg) + c→−3(
2
1
u
2
1
)+c
\sf \to - 3(2 {u}^{ \frac{ 1 }{2} } ) + c→−3(2u
2
1
)+c
\sf \to \: - 6( \sqrt{u} ) + c→−6(
u
)+c
Now put the value
\to \sf \: 1 - {r}^{3} = u→1−r
3
=u
We get
\sf \to - 6( \sqrt{1 - {r}^{3} } ) + c→−6(
1−r
3
)+c
Answer
\sf \to - 6( \sqrt{1 - {r}^{3} } ) + c→−6(
1−r
3
)+c
Step-by-step explanation:
Let the Cost Price be Rs a
Gain percent = 5 %
Selling price = 252
=> Cost Price + Gain = 252
=> a + 5 % of a = 252
=> a + 5a/ 100 = 252
=> a + a/20 = 252
=> 21a/20 = 252
=> a = 252 × 20 / 21
=> a = 12 × 20
=> a = 240
Cost Price = Rs 240
Now,
To get 35 % Gain,
Selling price = Cost Price + 35% of Cost Price
SP = 240 + 35× 240 / 100
SP = 240 + 7 × 12
SP = 240 + 84
SP = Rs 324
To get 35 % Profit, he should sell the tie in Rs 324
HOPE IT HELPS:)