Percentage - Study Mode
[#211] An army lost 10% of its men in war. 10% of the remaining died due to disease and 10% of the rest were declared disabled. Thus the strength of the army was reduced to 729000 active men. The original strength of the army was :
Correct Answer
(B) 1000000
Explanation
Solution: Initial number of soldiers in the army = x According to the question, $$eqalign{
& Rightarrow { ext{x}} imes frac{{90}}{{100}} imes frac{{90}}{{100}} imes frac{{90}}{{100}} = 729000 cr
& Rightarrow x = frac{{729000 imes 1000}}{{9 imes 9 imes 9}} cr
& Rightarrow x = 1000000 cr} $$ Alternate: 10% → $$frac{1}{10}$$ 10 → 9 in war 10 → 9 in disease 10 → 9 disabled 100 → 729 729 → 729000 1 → 1000 10000 → 1000 × 1000 = 1000000
[#212] In an examination, 35% of total students failed in Hindi, 45% failed in English and 20% failed in both. Find the percentage of those students who passed in both the subjects ?
Correct Answer
(D) 40%
Explanation
Solution: Failed students in Hindi = 35% Failed students in English = 45% Student failed in both subject hindi and english = 20% Student only fail in hind = 35 - 20 = 15% Student only fail in English = 45 - 20 = 25% Percentage of passed students in both subjects : = 100 - [ student fail in hindi + student fail in english + student fail in both subject] = [100 - (15 + 25 + 20)] = 40%
[#213] The price of an article was increased by r%. Later the new price was decreased by r%. If the latest price was Rs. 1, then the original price was :
Correct Answer
(D) Rs. $$left( {frac{{10000}}{{10000 - {r^2}}}}
ight)$$
Explanation
Solution: r% = $$frac{r}{100}$$ Initial Price Final 100 (100 + r) 100 (100 - r) 10000 (100 + r) (100 - r) According to the question, (100 + r) (100 - r) units = Rs. 1 (10000 - r 2 ) units = Rs. 1 1 unit = $$left( {frac{{1}}{{10000 - {r^2}}}}
ight)$$ Original price = $$left( {frac{{10000}}{{10000 - {r^2}}}}
ight)$$
[#214] The difference of two numbers is 15% of larger sum. The ratio of the larger number to the smaller number is :
Correct Answer
(A) 23 : 17
Explanation
Solution: Let the number are a and b where a > b According to the question, (a - b) = $$frac{15}{100}$$ (a + b) (a - b) = $$frac{3}{20}$$ (a + b) 20a - 20b = 3a + 3b 17a = 23b $$frac{a}{b}$$ = $$frac{23}{17}$$ Required ratio = 23 : 17
[#215] A number if reduced by 25% becomes 225. By what percent should it be increased so that it becomes 375 ?
Correct Answer
(A) 25%
Explanation
Solution: Let the number = x According to the question, $$frac{x × (100 - 25)}{100}$$ xa0 = 225 x = $$frac{225 × 100}{75}$$ x = 300 Required percentage : = $$frac{(375 - 300)}{300}$$ xa0 × 100 = 25%