using all digits 1,2,3,4 and 5 , fractional numbers are formed with exactly 2 digits in numerator and the remaining 3 digits in denominator. How many such Fractions will be greater than 1/4 in ratio? Eg : 54/123,12/543.
Answers
Given : using all digits 1,2,3,4 and 5 , fractional numbers are formed with exactly 2 digits in numerator and the remaining 3 digits in denominator.
To Find : How many such Fractions will be greater than 1/4 in ratio
Solution:
2 Digits out of 5 can be selected in ⁵C₂ = 10 ways
2 Digits in numerator can be arranged in 2! = 2 ways
and 3 Digits in Denominator can be arranged in 3! = 6 ways
Fractions greater than 1/4
=> greater than 25/100 , 50/200 , 75/300
As Denominator is > 100 Hence Numerator Tens Digit can not be 1 , 2
Also Denominator Hundred digit can not be 3 , 4 or 5
Possible Numerator 31 , 32 , 34 , 35 , 41 ,42 , 43 , 45 , 51 , 52 , 53 , 54
corresponding Denominators Less Than multiples of 4
124 , 128 , 136 , 140 , 164 , 168 , 172 , 180 , 204 , 208 , 212 , 216
Fraction greater than 1/4
with 31 and 32 numerator no possible combination
34/ 125 , 35/124 , 42/135 , 42/153 , 43/125 , 43/152 , 45/123 , 145/132
52/134 , 52/143 , 53/124 , 53/142 , 54/123 , 54/132 , 54/213
Hence 15 fractions greater than 1/4 in ratio are possible
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Answer:
Given : using all digits 1,2,3,4 and 5 , fractional numbers are formed with exactly 2 digits in numerator and the remaining 3 digits in denominator.
To Find : How many such Fractions will be greater than 1/4 in ratio
Solution:
2 Digits out of 5 can be selected in ⁵C₂ = 10 ways
2 Digits in numerator can be arranged in 2! = 2 ways
and 3 Digits in Denominator can be arranged in 3! = 6 ways
Fractions greater than 1/4
=> greater than 25/100 , 50/200 , 75/300
As Denominator is > 100 Hence Numerator Tens Digit can not be 1 , 2
Also Denominator Hundred digit can not be 3 , 4 or 5
Possible Numerator 31 , 32 , 34 , 35 , 41 ,42 , 43 , 45 , 51 , 52 , 53 , 54
corresponding Denominators Less Than multiples of 4
124 , 128 , 136 , 140 , 164 , 168 , 172 , 180 , 204 , 208 , 212 , 216
Fraction greater than 1/4
with 31 and 32 numerator no possible combination
34/ 125 , 35/124 , 42/135 , 42/153 , 43/125 , 43/152 , 45/123 , 145/132
52/134 , 52/143 , 53/124 , 53/142 , 54/123 , 54/132 , 54/213
Hence 15 fractions greater than 1/4 in ratio are possible
Step-by-step explanation: