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ICSE Class 8 Answered

The amount of work in a leather factory is increased by 50%. By what per cent is it necessary to increase the number of workers to complete the new amount of work in previously planned time, if the productivity of the new labour is 25% more.
Asked by kideuttam | 21 Jan, 2015, 10:00: PM
answered-by-expert Expert Answer
L e t space t h e space a m o u n t space o f space w o r k space o f space t h e space o r i g i n a l space l a b o u r space b e space apostrophe W apostrophe L e t space t h e space n u m b e r space o f space o r i g i n a l space l a b o u r space b e space apostrophe n apostrophe. L e t space t h e space p r o d u c t i v i t y space o f space t h e space o r i g i n a l space l a b o u r space b e space apostrophe p apostrophe. N e w space a m o u n t space o f space w o r k comma space W subscript 1 space equals space W plus space 50 over 100 cross times W equals fraction numerator 3 W over denominator 2 end fraction N e w space n u m b e r space o f space l a b o u r space equals space n subscript 1 N e w space p r o d u c t i v i t y space o f space l a b o u r space equals space p plus 25 over 100 cross times p equals fraction numerator 5 p over denominator 4 end fraction W e space k n o w comma space A m o u n t space o f space w o r k space equals space N u m b e r space o f space L a b o u r s space cross times space P r o d u c t i v i t y space cross times space T i m e T i m e space equals space fraction numerator A m o u n t space o f space W o r k over denominator N u m b e r space o f space L a b o u r s space cross times space P r o d u c t i v i t y end fraction fraction numerator W over denominator n cross times p end fraction equals fraction numerator W subscript 1 over denominator n subscript 1 cross times begin display style fraction numerator 5 p over denominator 4 end fraction end style end fraction rightwards double arrow fraction numerator W over denominator n cross times p end fraction equals fraction numerator begin display style fraction numerator 3 W over denominator 2 end fraction end style over denominator n subscript 1 cross times begin display style fraction numerator 5 p over denominator 4 end fraction end style end fraction rightwards double arrow n subscript 1 equals fraction numerator 6 n over denominator 5 end fraction % a g e space i n c r e a s e space i n space l a b o u r space equals space fraction numerator N e w space n o. space o f space l a b o u r s space minus space N u m b e r space o f space l a b o u r s over denominator N u m b e r space o f space l a b o u r end fraction cross times 100 equals fraction numerator space fraction numerator 6 n over denominator 5 end fraction minus n over denominator n end fraction cross times 100 equals fraction numerator space fraction numerator 6 n over denominator 5 end fraction minus n over denominator n end fraction cross times 100 equals 20 % N o. space o f space space l a b o u r space h a v e space t o space b e space i n c r e a s e d space b y space 20 % space i n space o r d e r space t h e space c o m p l e t e space t h e space w o r k space i n space t i m e.
Answered by Prasenjit Paul | 22 Jan, 2015, 10:51: AM

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