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प्रतिशत Difficult Questions and Answers | Page - 2

प्रतिशत


प्रतियोगी गणित

  1. सूरी अपने मासिक वेतन का 25% अपनी माँ को देती है। बचे हुए वेतन में से वह 15% किराए पर खर्च करती है तथा 25% मासिक खर्चों के लिए अपने पास रख लेती है। शेष बचे हुए धन को वह बैंक में जमा कर देती है। बैंक में जमा किए गए धन तथा माँ को दिए गए धन का योग रु 42000 है। उसका मासिक वेतन कितना है ?











  1. सुझाव देखें उत्तर देखें चर्चा करें

    माना सूरी का मासिक वेतन = रु P
    सूरी द्वारा अपनी माँ को दिया गया धन = P का 25% = P × ( 1/4 ) = रु P/4
    शेष धन = P - P/4 = 3P/4

    सही विकल्प: B

    माना सूरी का मासिक वेतन = रु P
    सूरी द्वारा अपनी माँ को दिया गया धन = P का 25% = P × ( 1/4 ) = रु P/4
    शेष धन = P - P/4 = 3P/4
    किराये पर खर्च धन = ( 3P/4 ) का 15% = ( 3P/4 ) × ( 3/20 ) =
    रु 9P/80
    मासिक खर्चों के लिए रखा धन = ( 3P/4 ) x ( 25/100 ) = रु 3P/16
    ∴ बैंक में जमा धन = ( 3P/4 ) - ( 9P/80 ) - ( 3P/16 ) = [ 60P - 9P - 15P ]/80 = 36P/80 = 9P/20
    अब , प्रश्नानुसार , ( P/4 ) + ( 9P/20 ) = 42000
    ⇒ ( 5P + 9P )/20 = 42000
    ⇒ 14P/20 = 42000
    ⇒ P = ( 42000 x 20 )/14 = 3000 x 20 = 60000

    अतः सूरी का मासिक वेतन = रु 60000 होगा ।


  1. इतिहास की परीक्षा में सम्पूर्ण कक्षा का औसत 80 अंक था। यदि 10% विद्यार्थियों ने 95 अंक अर्जित किए एवं 20% विद्यार्थियों ने 90 अंक , तो कक्षा में शेष विद्यार्थियों के अंकों का औसत कितना था ?









  1. सुझाव देखें उत्तर देखें चर्चा करें

    ∴ शेष विद्यार्थियों के अंकों औसत = ( शेष विद्यार्थियों के अंकों योग/शेष विद्यार्थियों की कुल संख्या ) x 100 %

    सही विकल्प: C

    माना कक्षा में विद्यार्थियों की कुल संख्या = 100
    तब , सभी विद्यार्थियों के अंकों का योग = 100 x 80 = 8000
    प्रश्नानुसार , 10% विद्यार्थियों ने 95 अंक प्राप्त किए।
    10 विद्यार्थियों के अंकों का योग = 10 x 95 = 950
    तथा 20% विद्यार्थियों ने 90 अंक प्राप्त किए।
    ∴ 20 विद्यार्थियों के अंकों का योग = 90 x 20 = 1800
    शेष विद्यार्थियों की कुल संख्या = 100 - 10 - 20 = 100 - 30 = 70
    शेष विद्यार्थियों के अंकों योग = 8000 - 950 - 1800 = 8000 - 2750 = 5250
    ∴ शेष विद्यार्थियों के अंकों औसत = ( शेष विद्यार्थियों के अंकों योग/शेष विद्यार्थियों की कुल संख्या ) x 100 %
    = ( 5250/70 ) x 100 % = 75
    अतः शेष विद्यार्थियों के अंकों औसत = 75 होगा ।



  1. एक व्यक्ति का मासिक वेतन रु 5180 है। खाद्य सामग्री तथा अन्य मदों में उसके खर्च का अनुपात 2 : 5 है। यदि खाद्य सामग्री के मूल्यों में 10% वृद्धि हो तथा अन्य मदों पर काम आने वाली वस्तुओं के मूल्यों में 15% वृद्धि हो , तो उस व्यक्ति के वेतन में कितनी वृद्धि की जाए कि उसकी विभिन्न मदों में खपत में कोई परिवर्तन न हो ?









  1. सुझाव देखें उत्तर देखें चर्चा करें

    खाद्य सामग्री तथा अन्य मदों में खर्च का अनुपात = 2 : 5
    माना खाद्य सामग्री पर खर्च = रु 2R
    तथा अन्य मदों पर खर्च = रु 5R
    तब प्रश्नानुसार , 2R + 5R = 5180

    सही विकल्प: D

    खाद्य सामग्री तथा अन्य मदों में खर्च का अनुपात = 2 : 5
    माना खाद्य सामग्री पर खर्च = रु 2R
    तथा अन्य मदों पर खर्च = रु 5R
    तब प्रश्नानुसार , 2R + 5R = 5180
    ⇒ 7R = 5180
    ⇒ R = 5180/7 = रु 740
    खाद्य सामग्री पर खर्च = 2 x 740 = रु 1480
    तथा अन्य मदों पर खर्च = 5 x 740 = रु 3700
    खाद्य सामग्री के मूल्यों में वृद्धि के बाद मूल्य = 1480 + 1480 का 10%
    = 1480 + 1480 x (10/100 ) = 1480 + 148 = रु 1628
    अन्य मदों के मूल्यों में वृद्धि के बाद मूल्य = 3700 + 3700 का 15%
    = 3700 + 3700 x 3/20 = 3700 + 555 = रु 4255
    ∴ व्यक्ति के वेतन में वृद्धि =रु ( 1628 + 4255 ) - 5180
    = ( 5883 - 5180 ) = रु 703
    अतः व्यक्ति के वेतन में वृद्धि = रु 703 होगी।


  1. एक विद्यालय में 72% कर्मचारी चाय तथा 44% कर्मचारी कॉफ़ी पीते हैं। यदि प्रत्येक कर्मचारी चाय या कॉफ़ी अवश्य पीता हो तथा 40 कर्मचारी चाय तथा कॉफ़ी दोनों पीते हों ,तो उस विद्यालय में कुल कितने कर्मचारी हैं ?









  1. सुझाव देखें उत्तर देखें चर्चा करें

    माना कुल कर्मचारियों की संख्या = 100
    तब , चाय न पीने वाले कर्मचारियों की संख्या = ( 100 - 72 ) = 28
    कॉफ़ी न पीने वाले कर्मचारियों की संख्या = ( 100 - 44 ) = 56
    चाय तथा कॉफ़ी दोनों पीने वाले कर्मचारियों की संख्या = 100 - ( 28 + 56 ) = 100 - 84 = 16

    सही विकल्प: C

    माना कुल कर्मचारियों की संख्या = 100
    तब , चाय न पीने वाले कर्मचारियों की संख्या = ( 100 - 72 ) = 28
    कॉफ़ी न पीने वाले कर्मचारियों की संख्या = ( 100 - 44 ) = 56
    चाय तथा कॉफ़ी दोनों पीने वाले कर्मचारियों की संख्या = 100 - ( 28 + 56 ) = 100 - 84 = 16
    जब 16 कर्मचारी चाय व कॉफ़ी दोनों पीते हों , तब कुल कर्मचारियों की संख्या = 100
    जब 1 कर्मचारी चाय व कॉफ़ी दोनों पीते हों , तब कुल कर्मचारियों की संख्या = 100/16
    ∴ जब 40 कर्मचारी चाय व कॉफ़ी दोनों पीते हों , तब कुल कर्मचारियों की संख्या = ( 100/16 ) x 40 = 25 x 10 = 250

    अतः कुल कर्मचारियों की संख्या 250 होगी।



  1. एक व्यक्ति अपनी आय के 10% की बचत करता है , किन्तु 2 वर्ष बाद जब उसकी आय 20% बढ़ गई , तब भी वह पहले जितनी ही राशि की बचत कर सका। उसका व्यय कितने प्रतिशत बढ़ गया है ?









  1. सुझाव देखें उत्तर देखें चर्चा करें

    माना व्यक्ति की मूल आय = रु A
    तब , बचत = A का 10% = A × 1/10 = रु A/10
    प्रारंभिक खर्च = A - A/10 = रु 9A/10

    सही विकल्प: A

    माना व्यक्ति की मूल आय = रु A
    तब , बचत = A का 10% = A × 1/10 = रु A/10
    प्रारंभिक खर्च = A - A/10 = रु 9A/10
    2 वर्ष बाद , जब बढ़ जाती है।
    तब , नई आय = A × 120% = रु 12A/10
    बचत = रु A/10
    ∴ नया खर्च = नई आय - बचत
    = 12A/10 - A/10 = रु 11A/10
    व्यय प्रतिशत = [ { ( 11A/10 ) - ( 9A/10 ) }/9A/10 ] x 100 %
    = 200/9 % = 222/9 %
    अतः व्यक्ति का व्यय प्रतिशत 222/9 % बढ़ गया है।