Percentage - Study Mode

[#136] 80% of a smaller number is 4 less than 40% of a larger number. The larger number is 85 greater than the smaller one. The sum of these two number is
Correct Answer

(C) 235

Explanation

Solution: Let the smaller number be x and larger number be y According to the question, 80% of x + 4 = 40% of y 4y - 8x = 40 y - 2x = 10 --------- (1) y - x = 85 ----------- (2) By using (1) and (2), we get x = 75 y = 160 x + y = 235

[#137] A number x is mistakenly divided by 10 instead of being multiplied by 10. what is the percentage error in the result?
Correct Answer

(A) -99%

Explanation

Solution: Actual result = 10x By mistake it has been divided by 10 = $$frac{x}{{10}}$$ %Change = $$ {frac{{10x - left( {frac{{10}}{x}}
ight)}}{{10x}}} $$ xa0 × 100 = 99 = -99% Since, actual value is greater than the wrong value. Alternatively, Let, x = 10 Actual result = 10 × 10 = 100 Wrong result = $$frac{{10}}{{10}}$$ = 1 Change = (1 - 100) = -99 % Change = - 99%

[#138] 5 kg of metal A and 20 kg of metal B are mixed to form an alloy. The percentage of metal A in the alloy is ?
Correct Answer

(A) 20%

Explanation

Solution: Weight of metal A = 5kg Total weight of the alloy : = (5 + 20) kg = 25 kg ∴ Required percentage : $$eqalign{
& = left( {frac{5}{{25}} imes 100}
ight)\% cr
& = 20\% cr} $$

[#139] 23% of 8040 + 42% of 545 = ? % of 3000
Correct Answer

(C) 69.27

Explanation

Solution: Let 23% of 8040 + 42% of 545 = x% of 3000 Then, $$left( {frac{{23}}{{100}} imes 8040}
ight) + left( {frac{{42}}{{100}} imes 545}
ight)$$ xa0 xa0 xa0 = $$left( {frac{x}{{100}} imes 3000}
ight)$$ $$eqalign{
& Rightarrow 30x = 1849.2 + 228.9 cr
& Rightarrow 30x = 2078.1 cr
& Rightarrow x = frac{{2078.1}}{{30}} cr
& Rightarrow x = 69.27 cr} $$

[#140] While purchasing one item costing Rs. 400, I had to pay the sales tax at 7% and on another costing Rs. 6400, the sales tax was 9%. What percent of the sales tax I had to pay, taking the two items together on an average ?
Correct Answer

(C) $$8frac{15}{17}$$%

Explanation

Solution: Total sales tax paid = 7% of Rs. 400 + 9% of Rs. 6400 = Rs. $$left( {frac{7}{{100}} imes 400 + frac{9}{{100}} imes 6400}
ight)$$ = Rs. (28 + 576) = Rs. 604 Total cost o the items : = Rs. (400 + 6400) = Rs. 6800 ∴ Required percentage $$eqalign{
& = left( {frac{{604}}{{6800}} imes 100}
ight)\% cr
& = 8frac{{15}}{{17}}\% cr} $$