Percentage - Study Mode

[#366] In Sabarmati Express, there as many wagons as there are the no. of seats in each wagon and not more than one passenger can have the same berth (seat). If the middlemost compartment carrying 25 passengers is filled with 71.428% of its capacity, then find the maximum no. of passengers in the train that can be accommodated if it has minimum 20% seats always vacant.
Correct Answer

(C) 980 seats

Explanation

Solution: Total number of passenger in each compartment = $$frac{{ {25 imes 7} }}{5}$$xa0 = $$35$$ Total berth = 35 2 = 1225 Maximum available capacity $$eqalign{
& = frac{{ {1225 imes 80} }}{{100}} cr
& = 980,{ ext{seats}} cr} $$

[#367] The population of a village is 5000 and it increases at the rate of 2% every year. After 2 years, the population will be:
Correct Answer

(B) 5202

Explanation

Solution: $$eqalign{
& { ext{Population after two years}}, cr
& = 5000 imes {left[ {1 + {frac{2}{{100}}} }
ight]^2} cr
& = 5202 cr
& { ext{Alternatively}}, cr
& 5000 = = 2\% uparrow Rightarrow 5100 = = 2\% uparrow Rightarrow 5202 cr} $$

[#368] In a class, the no. of boys is more than the no. of girls by 12% of the total strength. The ratio of boys and girls is:
Correct Answer

(C) 14 : 11

Explanation

Solution: Let the no. of total student in the class = 100 and number of boy = X
and 12% of the 100 is 12 Number of girl is x - 12 total number of student is x + (x - 12) = 100 therefore x = 56. Then, No of boys = 56
No. of girls = 44
Boys : Girls = 56 : 44 = 14 : 11

[#369] In an office there were initially N employees. The HR manager first hired P% employees then after a month Q% employees left the office, the value of (P - Q) is:
Correct Answer

(B) $$frac{{{ ext{PQ}}}}{{100}}$$

Explanation

Solution: $$eqalign{
& frac{{ ext{P}}}{{100 + { ext{P}}}} = frac{{ ext{Q}}}{{100}} cr
& { ext{or}},,100left( {{ ext{P}} - { ext{Q}}}
ight) = { ext{PQ}} cr
& { ext{or}},,left( {{ ext{P}} - { ext{Q}}}
ight) = frac{{{ ext{PQ}}}}{{100}} cr} $$

[#370] The amount of work in a leather factory is increased by 50%. By what percent is it necessary to increase the number of workers to complete the new amount of work in previously planned time, if the productivity of the new labour is 25% more.
Correct Answer

(C) 40%

Explanation

Solution: Men × Time = Work
100 × 1 = 100 unit work
150 × 1 = 150 unit work
Extra man power = 50 But since, new workers are $$frac{5}{4}$$ time as efficient as existing workers Thus, Actual no. of workers = $$frac{{50}}{{frac{5}{4}}}$$ = 40 workers % required = $$frac{{40 imes 100}}{{100}} = 40\% $$