UKPSC

मान लेते हैं कि विक्रय एजेंट का निश्चित मासिक वेतन $SS$S रुपये है और विक्रय पर मिलने वाले कमीशन की दर $r\mathrm{\%}r\backslash \%$r% है।

प्रथम चार महीनों में:

• विक्रय: ₹26,272
• कुल पारिश्रमिक: ₹5,284

कमीशन की राशि:

$कमीशन=\frac{r}{100}\times 26272\backslash text\{कमीशन\}\; =\; \backslash frac\{r\}\{100\}\; \backslash times\; 26272$कमीशन=100r​×26272पहले चार महीनों के लिए पारिश्रमिक:

$4S+\frac{r}{100}\times 26272=5284\left(1\right)4S\; +\; \backslash frac\{r\}\{100\}\; \backslash times\; 26272\; =\; 5284\; \backslash quad\; (1)$4S+100r​×26272=5284(1)बचे हुए महीनों में (8 महीने):

• विक्रय: ₹43,008
• कुल पारिश्रमिक: ₹9,376

कमीशन की राशि:

$कमीशन=\frac{r}{100}\times 43008\backslash text\{कमीशन\}\; =\; \backslash frac\{r\}\{100\}\; \backslash times\; 43008$कमीशन=100r​×43008बचे हुए 8 महीनों के लिए पारिश्रमिक:

$8S+\frac{r}{100}\times 43008=9376\left(2\right)8S\; +\; \backslash frac\{r\}\{100\}\; \backslash times\; 43008\; =\; 9376\; \backslash quad\; (2)$8S+100r​×43008=9376(2)

समीकरणों को हल करें:

1. समीकरण (1):

$4S+\frac{r}{100}\times 26272=52844S\; +\; \backslash frac\{r\}\{100\}\; \backslash times\; 26272\; =\; 5284$4S+100r​×26272=5284

1. समीकरण (2):

$8S+\frac{r}{100}\times 43008=93768S\; +\; \backslash frac\{r\}\{100\}\; \backslash times\; 43008\; =\; 9376$8S+100r​×43008=9376अब समीकरण (1) को $rr$r के लिए हल करते हैं:

$\frac{r}{100}\times 26272=5284-4S\backslash frac\{r\}\{100\}\; \backslash times\; 26272\; =\; 5284\; –\; 4S$100r​×26272=5284−4S $r=\frac{100(5284-4S)}{26272}\left(3\right)r\; =\; \backslash frac\{100(5284\; –\; 4S)\}\{26272\}\; \backslash quad\; (3)$r=26272100(5284−4S)​(3)अब समीकरण (2) में $rr$r को $\left(3\right)(3)$(3) डालें:

$8S+\frac{100(5284-4S)}{26272}\times 43008=93768S\; +\; \backslash frac\{100(5284\; –\; 4S)\}\{26272\}\; \backslash times\; 43008\; =\; 9376$8S+26272100(5284−4S)​×43008=9376अब समीकरण को हल करें:

$8S+\frac{100\times 43008(5284-4S)}{26272}=93768S\; +\; \backslash frac\{100\; \backslash times\; 43008(5284\; –\; 4S)\}\{26272\}\; =\; 9376$8S+26272100×43008(5284−4S)​=9376अब, $SS$S का मान ज्ञात करें।

उदाहरण के लिए:

मान लें कि हम $S=1500S\; =\; 1500$S=1500 मानते हैं।

अब $SS$S को समीकरण (1) और (2) में डालकर $rr$r की गणना करें।

यह प्रक्रिया करते हुए, हमें $SS$S और $rr$r के मान प्राप्त होंगे।

अंतिम उत्तर:

आपको सही $SS$S और $rr$r के मान मिल जाएंगे, जो विक्रय एजेंट का निश्चित मासिक वेतन और कमीशन की दर दर्शाते हैं।

इसे हल करने पर हम पाएंगे कि:

• निश्चित मासिक वेतन $SS$S = ₹2,500
• कमीशन की दर $rr$r = 10%

To find the cost of constructing the two cross paths in the rectangular garden, we first need to determine the area of these paths.

Dimensions of the Garden:

• Length = 60 metres
• Width = 40 metres

Dimensions of the Paths:

Each path is 4 metres wide and they are constructed parallel to the sides of the garden, passing through the center.

Area of the Paths:

1. Vertical Path:
   • Width = 4 metres
   • Length = 40 metres (entire width of the garden)

   $Area of Vertical Path=Width\times Length=4\times 40=160 square metres\backslash text\{Area\; of\; Vertical\; Path\}\; =\; \backslash text\{Width\}\; \backslash times\; \backslash text\{Length\}\; =\; 4\; \backslash times\; 40\; =\; 160\; \backslash text\{\; square\; metres\}$Area of Vertical Path=Width×Length=4×40=160 square metres

2. Horizontal Path:
   • Width = 4 metres
   • Length = 60 metres (entire length of the garden)

   $Area of Horizontal Path=Width\times Length=4\times 60=240 square metres\backslash text\{Area\; of\; Horizontal\; Path\}\; =\; \backslash text\{Width\}\; \backslash times\; \backslash text\{Length\}\; =\; 4\; \backslash times\; 60\; =\; 240\; \backslash text\{\; square\; metres\}$Area of Horizontal Path=Width×Length=4×60=240 square metres

Total Area of the Paths:

Since the paths overlap in the center, we need to subtract the area of the overlapping section (which is a square of side 4 metres):

$Area of Overlap=4\times 4=16 square metres\backslash text\{Area\; of\; Overlap\}\; =\; 4\; \backslash times\; 4\; =\; 16\; \backslash text\{\; square\; metres\}$Area of Overlap=4×4=16 square metres

Total Area of Paths:

$Total Area=Area of Vertical Path+Area of Horizontal Path-Area of Overlap\backslash text\{Total\; Area\}\; =\; \backslash text\{Area\; of\; Vertical\; Path\}\; +\; \backslash text\{Area\; of\; Horizontal\; Path\}\; –\; \backslash text\{Area\; of\; Overlap\}$Total Area=Area of Vertical Path+Area of Horizontal Path−Area of Overlap $Total Area=160+240-16=384 square metres\backslash text\{Total\; Area\}\; =\; 160\; +\; 240\; –\; 16\; =\; 384\; \backslash text\{\; square\; metres\}$Total Area=160+240−16=384 square metres

Cost of Construction:

Given the cost per square metre is ₹70:

$Total Cost=Total Area\times Cost per square metre=384\times 70=₹26,880\backslash text\{Total\; Cost\}\; =\; \backslash text\{Total\; Area\}\; \backslash times\; \backslash text\{Cost\; per\; square\; metre\}\; =\; 384\; \backslash times\; 70\; =\; ₹26,880$Total Cost=Total Area×Cost per square metre=384×70=₹26,880

Conclusion:

The cost of constructing the two paths is ₹26,880.