Here to say which fraction is greater from the given options, the fraction with greater numerator with same denominator or smaller denominator with same numerator.
To find the greater fraction, among the given options, make the denominators same for the options by finding the LCM of all the denominators.
7/12, 9/16, 13/20, 32/80
Now, LCM of 12, 16, 20, 80 = 240.
Then,
140/240, 135/240, 156/240, 96/240
Here
Hence, largest fraction = 13/20.
According to question , we have
?( x - 0 )2 + ( 0 + 5 )2 = 13
? x2 + 25 = 169
? x2 = 169 - 25 = 144
? x = ?144 = 12
Exp. =log3228 + log24337 - log361296
= log25 28 + log35 37 - log36 362
= (8/5)log22 + (7/5)log33 - 2log3636
= 8/5 + 7/5 - 2 = 1
In a quadrilateral ABCD,
Given :- ?B = 90°
AB2 + BC2 + CD2 = AC2 + CD2 = AD2 { ? In triangle ABC , AB2 + BC2 = AC2 }
So, in triangle ACD, angle opposite to AD = 90° ( by Converse of Pythagoras theorem)
? ?ACD = 90°
Let 31% of A = 46.5
? (31 x A)/100 = 46.5
? A = (46.5 x 100) / 31 = 150
(A + B)'s 1 day's work = 1/18
(B + C)'s 1 day's work = 1/24
(A + C)'s 1 day's work = 1/36
Adding 2 (A + B + C)'s 1 day's work = (1/18 + 1/24 + 1/36) = 1/8
? (A + B + C)'s day's work = 1/16
Hence, all working together can finish it in 16 days.
let the fixed charges = ? p for first 5 km
and the additional charges = ? q per km
according to the question
p + 5q = 350........... (1)
p + 20q = 800...........(2)
on subtracting Eq. 1 from Eq. 2 we get
15q = 450
q = 30
On putting the value of q in Eq. (1) we get
p = 200
? charge for a distance of 30 km = p + 25q
= 200 + 30 x 25 = ? 950
The given question is,
(70 ÷ 100)? + 3 = (0.49)4 x (0.343)4 ÷ (0.2401)4
As we know that
70 ÷ 100 = 0.7
0.49 = 0.7 2
0.343 = 0.7 3
0.2401 = 0.7 4
Put these value in given question , we will get
? (0.7)? + 3 = (0.72)4 x ( 0.73 )4 ÷ ( 0.74 )4
? (0.7) ? + 3 = 0.7 2 x 4 x 0.7 3 x 4 ÷ 0.7 4 x 4
? (0.7) ? + 3 = 0.7 8 x 0.7 12 ÷ 0.7 16
Apply the law of Fractional Exponents and Laws of Exponents
(am)(an) = am+n
am÷an=am-n
Or
am/an=am - n
we will get,
? (0.7)? + 3 = (0.7) 8 + 12 - 16
? (0.7)? + 3 = (0.7) 20 - 16
? (0.7)? + 3 = (0.7) 4
On comparing the exponents both sides, we get
? + 3 = 4
? ? = 4 - 3 = 1
Given in the question,
n(H ? E) = 1000, n(H) = 750, n(E) = 400
Use the below formula,
n(H ? E) = n(H) + n(E) ? n(H ? E)
We get 1000 = 750 + 400 ? n(H ? E)
? n(H ? E) = 1150 ? 1000 = 150.
Number of People who can speak Hindi only
= n(H ? E?) = n(H) ? n(H ? E)
= 750 ? 150 = 600.
Let Ram spends p minute on each Mathematics question.
According to the question.
50 x p + 100 x p/2 + 50 x p/2 = 3 x 60
p(50+ 50 + 25) = 180
? p = 180/125
? Required time = 50 x 180/125
? Required time = 2 x 180/5
? Required time = 2 x 36 = 72 min
Method 2
Let Ram spends a minute on each sciences and Gk questions.
According to the question,
50 x 2a + 150 x a = 3 x 60
100a + 150a = 180
250a = 180
a = 180/250
So total time spend on Mathematics question = 2a x 50 question
So total time spend on Mathematics question = 2 x 50 x 180/250 = 72 minutes
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