Percentage - Study Mode

[#101] For an examination it is required to get 36% of maximum marks to pass. A student got 113 marks and failed by 85 marks. The maximum marks for the examination are:
Correct Answer

(B) 550

Explanation

Solution: 36% marks = 113 + 85 ⇒ 36% marks = 198 So, ⇒ 1% marks = $$frac{{198}}{{36}}$$ = 5.5 ⇒ 100% marks = 5.5 × 100 = 550

[#102] 1% of 1% of 25% 1000 is:
Correct Answer

(A) 0.025

Explanation

Solution: $$eqalign{
& 1\% ,{ ext{of}},1\% ,{ ext{of}},25\% ,1000 cr
& = 1\% ,{ ext{of}},1\% ,{ ext{of}},, {frac{{ {25 imes 1000} }}{{100}}} cr
& = 1\% ,{ ext{of}},1\% ,{ ext{of}},250 cr
& = 1\% ,{ ext{of}},, {frac{{ {1 imes 200} }}{{100}}} cr
& = 1\% ,{ ext{of}},,2.5 cr
& = frac{{2.5}}{{100}} cr
& = 0.025 cr} $$

[#103] The population of a village increase by 5% annually. If its present population is 4410, then its population 2 years ago was:
Correct Answer

(B) 4000

Explanation

Solution: Using compounding formula $${ ext{a}} + { ext{b}} + frac{{{ ext{ab}}}}{{100}}$$ we have $$eqalign{
& 5 + 5 + frac{{25}}{{100}} cr
& = 10.25\% cr} $$ so if the population 2 yrs ago be x then $$eqalign{
& { ext{x}} + frac{{10.25x}}{{100}} = 4410 cr
& { ext{or}},,110.25{ ext{x}} = 441000 cr
& herefore { ext{x}} = 4000 cr} $$

[#104] A spider climbed $$frac{{125}}{2}$$ % of the height of the pole in one hour and in the next hour it covered $$frac{{25}}{2}$$ % of remaining height. If pole's height is 192 m, then distance climbed in second hour is:
Correct Answer

(D) 9m

Explanation

Solution: $$eqalign{
& { ext{Height}},{ ext{of}},{ ext{the}},{ ext{Pole}} = 192,m. cr
& { ext{Spider}},{ ext{covered}},{ ext{in}},{ ext{first}},{ ext{hour}}, cr
& = frac{{125}}{2}\% ,of,192 cr
& = frac{{ {125 imes 192} }}{{ {2 imes 100} }} cr
& = 120,m cr
& { ext{Remaining Pole}} = 192 - 120 = 72,m cr
& { ext{Spider}},{ ext{covered}},{ ext{in}},{ ext{second}},{ ext{hour}}, cr
& = frac{{25}}{2}\% ,{ ext{of}},{ ext{ remaining}},{ ext{ height}} cr
& = frac{{ {25 imes 72} }}{{ {2 imes 100} }} cr
& = 9,m cr} $$

[#105] What is a percent of b divided by b percent of a?
Correct Answer

(C) 1

Explanation

Solution: $$eqalign{
& a,{ ext{percent}},{ ext{of}},b cr
& = {frac{a}{{100}}} imes b = {frac{{ab}}{{100}}} cr
& b,{ ext{percent}},{ ext{of}},a cr
& = {frac{b}{{100}}} imes a = {frac{{ab}}{{100}}} cr
& { ext{on}},{ ext{division}},{ ext{we}},{ ext{get}},1 cr} $$