In a city, 40.1% of the adults are illiterate while 85.1% of the children are...

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Question Id : 9481 | Context :NIMCET 2020

Question

In a city, 40.1% of the adults are illiterate while 85.1% of the children are literate. If the ratio of the adults to that of the children is 2:3, then what percent of the population is literate?

🎥 Video solution / Text Solution of this question is given below:

Assume total population = 100.

Given, ratio of adults to children = 2:3.

Thus,
Adults =

25×100=40<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>5</mn></mfrac><mo>×</mo><mn>100</mn><mo>=</mo><mn>40</mn></math>

Children =

35×100=60<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>5</mn></mfrac><mo>×</mo><mn>100</mn><mo>=</mo><mn>60</mn></math>

Among adults:
Literate adults =

59.9 % <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>59.9</mn><mi mathvariant="normal">%</mi></math>

of 40 =

59.9100×40=23.96<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mn>59.9</mn><mn>100</mn></mfrac><mo>×</mo><mn>40</mn><mo>=</mo><mn>23.96</mn></math>

Among children:
Literate children =

85.1 % <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>85.1</mn><mi mathvariant="normal">%</mi></math>

of 60 =

85.1100×60=51.06<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mn>85.1</mn><mn>100</mn></mfrac><mo>×</mo><mn>60</mn><mo>=</mo><mn>51.06</mn></math>

Total literate people =

23.96 + 51.06 = 75.02 <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mn>23.96</mn><mo>+</mo><mn>51.06</mn><mo>=</mo><mn>75.02</mn></math>

Thus, percentage of literates =

75.02100×100=75.02%≈75%<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mn>75.02</mn><mn>100</mn></mfrac><mo>×</mo><mn>100</mn><mo>=</mo><mn>75.02</mn><mi mathvariant="normal">%</mi><mo>≈</mo><menclose notation="box"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mn>75</mn><mi mathvariant="normal">%</mi></mrow></mstyle></mrow></menclose></math>

Question

In a city, 40.1% of the adults are illiterate while 85.1% of the children are literate. If the ratio of the adults to that of the children is 2:3, then what percent of the population is literate?

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