Test: Percentages - 2 - UGC NET MCQ

Let A = set of students who play football and 

B = set of students play cricket. 

Then n(A) = 40, n (B) = 50 and 

n(A U B) = (100 - 18) = 82 

n(A U B) = n(A) + n(B) “ n(A ∩ B) 

n(A∩B) = n(A) + n(B) “ n(AUB) = (40 + 50 -82) = 8 

Percentage of the students who play both = 8%

Reduction % in consumption = {r/(100+ r) Ã -100}%
= (25/125 Ã - 100)%
= 20%

Let the original fraction be x/y. 
Then new fraction

Therefore 24/25(x/y) = 4/15 
⇒ x/y = (4/15 Ã - 25/24) = 5/18 
Therefore Original Fraction = 5/18

Let the weight of fresh grapes be x kg 
Quantity of water in it = (80/100 Ã - x)kg = 4x/5 kg 
Quantity of pulp in it = (x “ 4x/5)kg = x/5 kg 
Quantity of water in 250 kg dry grapes 
= (10/100 Ã- 250)kg = 25kg 
Quantity of pulp in it = (250 - 25)kg = 225 kg 
Therefore, x/5 = 225 
⇒ x = 1125

Total candidates = (100 + 75) = 175 
Total passed = (75/100 Ã- 100) + (60/100 Ã- 75) 
= (75 + 45) = 120 
Therefore Pass % = (120/175 Ã -100)% 
= 480/7 % = 68 4/7 %

Let the number be x and (2490 - x). 
Then 6.5 % of x = 8.5 % of (2490 - x) 
⇒ 6.5/100 Ã - x = 8.5/100 Ã - (2490 - x) 
⇒ 65x/1000 = 85(2490 - x)/1000 
⇒ 65x = (85 Ã - 2490) “ 85x 
⇒ 150x =(85 Ã - 2490) 
⇒ x = 211650/150 = 1411 
Hence the numbers are 1411 and (2490 - 1411) = 1079

Let the total number of voters be x 
Votes cast = 92 % of x = (92/100 Ã - x) = 23x/25
Votes in favour of winning candidate = 48/100 Ã - x 
= 12x/25
Votes polled by defeated candidate = (23x/25 “ 12x/25) 
= 11x/25 12x/25 “ 11x/25 = 1100 
⇒ 12x “ 11x = 27500 
⇒ x = 27500

Let n erasers be available for a rupee 
Reduced Price = (75/100 Ã - 1) = Re ¾ 
3/4 rupee fetch n erasers = 1 Rupee will fetch (n à - 4/3) erasers 
Therefore, 4n/3 = n +2 ⇒ 4n = 3n +6 ⇒ n =6

Let length = x units and breadth = Y units 
Then actual area = xy sq.units 
Length shown = (105/100 Ã - x)units = 21x/20 units; 
Breadth shown = (103/100 Ã - Y) 
Calculated area = (21x/20 Ã - 103y/100)sq.units 
Error = 2163xy/2000 sq.units 
Error = (2163xy/2000 - xy) 
Error = 163xy/2000 
Error % = (163xy/2000 à - 1/xy à - 100)% 
= 163/20 % = 8.15 %

Quantity of water in 100kg of fresh fruits =(68/100 × 100)kg 
Quantity of pulp in it = (100 - 68)kg = 32 kg 
Let the dry fruit be x kg 
Water in it = (20/100 Ã - x)kg = x/5 kg 
Quantity of pulp in it = (x “ x/5)kg = 4x/5 kg 
Therefore, 4x/5 = 32 ⇒ x = 160/4 = 40 kg