Let total journey be y km.
From question y/35 - y/40= 15/60
? y = ( 35 x 40 )/ ( 4 x 5 ) = 70
? Total Journey = 70 km
Let total journey = y km
Total time taken = time taken during 60% of distance + time taken during 20% of distance + time taken in remaining distance
= [( 60y / 100 ) / 30] + [( 20y / 100 ) / 20] + [( 20y / 100 ) / 10]
= ( y / 50 + y / 100 + y / 50 )hrs
= y/20 hours.
Average speed = total distance traveled / total time taken.
= [y / ( y/20 )] km/hr
=20 km/hr.
sum of odd number upto 100 = 1 + 3 + 5 + 7+....+ 95 + 97 + 99
=(1+99) + (3+97) + (5+95) +.... upto 25 terms
= 100 + 100 + 100 +.... upto 25 terms
= 2500
Average = 2500 /50
= 50
Age of A : age of B : age of C = 3 : 5 : 7
So the average age of 3 boys (3x + 5x + 7x ) /3 = 15
?15x= 15 x 3
? x= 3
Average cost =( w1x1 + w2x2 + w3x3 ) / (w1 +w2 +w3)
= ( 1200 x 30 +1500 x 25 + 2000 x 32) / ( 1200 + 1500 + 2000 )
= 137500 / 4700
= ? 29.25 per kg
a + b + c = 11 x 3 = 33 .....(i)
c + d + e = 17 x 3 = 51 .....(ii)
e + f = 22 x 2 = 44 .....(iii)
e + c = 17 x 2 = 34 .....(iv)
From Eqs. (ii) and (iv), we get
34 + d = 51
? d = 17
Now adding Eqs. (i), (ii), (v), we get
a + b + c + d + e + f = 33 + 44 + 17 = 94
? Average of a, b, c, d, e and f = 94/6 = 152?3
New sum of numbers = previous sum - 26 + 36
=10 x 15 - 26 + 36
= 160
? Correct Average = 160 / 10 = 16.
Seventh Result = sum of first 7 results + sum of last 7 results - sum of all 13 results.
? Seventh Result = (7 x 63) + (7 x 70) - (13 x 68 )
=47
Thirteenth Result = sum of all 25 results - sum of first 12 results - sum of last 12 results.
= 25 x 18 - 12 x 14 ? 12 x 17
=78
From question
M + T + W + TH = 4 x 38° = 152°
? T + W + TH =152° ? 30° = 122°
Again from question
? T + W + TH + F = 4 x 40° = 160°
? F = 160° ? 122°
= 38°
Sum of 5 consecutive integers
x + ( x +1 ) + ( x +2 ) + ( x + 3 ) + ( x +4 ) = 5n
? 5x + 10 = 5n
? x = ( n ? 2 ) ......(i)
Average of 7 consecutive integers
= [( 5x + 10 ) + ( x + 5 ) + ( x + 6 )] / 7
= 7x + 21 / 7
= x + 3 .....(ii)
from eq. (i) and (ii)
New average = x + 3 = ( n ? 2 + 3 ) = n + 1
So , the new average increases by 1 .
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