51. The sum of 15% of a positive number and 20% of the same number is 126. What is one-third of that number?
(a) 360
(b) 1080
(c) 120
(d) 40
(e) None of these
Solution: (c)
(15% + 20%) of x = 126
\(\displaystyle x=\frac{{126\times 100}}{{35}}=360\)
Therefore, required answer = \(\displaystyle 360\times \frac{1}{3}=120\)
52. Nandita scored 80% marks in five subjects together viz Hindi, Science, Maths, English and Sanskrit, where in the maximum marks of each subject were 105. How many marks did Nandita score in Science if she scored 89 marks in Hindi, 92 marks in Sanskrit, 98 marks in Maths and 81 marks in English?
(a) 60
(b) 75
(c) 65
(d) 70
(e) None of these
Solution: (a)
(Total marks scored by Nandita =\(\displaystyle 525\times \frac{{80}}{{100}}=420\)
Let Score in Science be x
89 + 92 + 98 + 81 + x = 420
360 + x = 420
\(\displaystyle \Rightarrow \)x = 60
53. Niraj incurred a loss of 55 percent on selling an article for ₹ 9,549. What was the cost price of the article?
(a) ₹ 27,700
(b) ₹ 25,600
(c) ₹ 21,220
(d) ₹ 29,000
(e) None of these
Solution: (c)
Let cost Price of article be x
\(\displaystyle x-\frac{{55}}{{100}}x=9549\)
\(\displaystyle \frac{{45x}}{{100}}=9549\)
x=\(\displaystyle \frac{{9549\times 100}}{{45}}=21220\)
54. In order to pass in an exam, a student is required to get 780 marks out of the aggregate marks. Sonu got 728 marks and was declared failed by 5 percent. What are the maximum aggregate marks a student can get in the examination?
(a) 1040
(b) 1100
(c) 1000
(d) Cannot be determined
(e) None of these
Solution: (a)
5% of maximum aggregate marks = 780 – 728 = 52
Let maximum aggregate marks be x
5% of x = 52
Maximum aggregate marks = \(\displaystyle \frac{{52}}{5}\times 100=1040\)
55. The sum of 15% of a positive number and 10% of the same number is 70. What is twice of that number?
(a) 440
(b) 280
(c) 560
(d) 140
(e) None of these
Solution: (c)
Let the positive no. be x.
According to question. 15% of x + 10% of x = 70
\(\displaystyle x\times \frac{{15}}{{100}}+\frac{{x\times 10}}{{100}}=70\)
\(\displaystyle \frac{{15x}}{{100}}+\frac{{10x}}{{100}}=70\)
\(\displaystyle \frac{{24x}}{{100}}=70\)
x= \(\displaystyle \frac{{70\times 100}}{{25}}=280\)
Therefore, Double of the given number = 280 × 2 = 560
56. In order to pass in an exam a student is required to get 975 marks out of the aggregate marks. Priya got 870 marks and was declared failed by 7 percent. What are the maximum aggregate marks a student can get in the examination?
(a) 1500
(b) 1000
(c) 1200
(d) Cannot be determined
(e) None of these
Solution: (a)
Minimum marks to pass = 975
Priya failed by 975 – 870 = 105 marks
Maximum marks = \(\displaystyle \frac{{105}}{7}\times 100=1500\)
57. A salesgirl’s terms were changed from a flat commission of 5% on all her sales to a fixed salary of ₹ 1000 plus 2.5% commission on all sales exceeding ₹4000. If her remuneration as per the new scheme was ₹600 more than that by the previous scheme, her total sales was
58. The product of one-third of a number and 150% of another number is what percent of the product of the original numbers?
(a) 80%
(b) 50%
(c) 75%
(d) 120%
(e) None of these
Solution: (b)
Let the original numbers be x and y and their product be xy
Product of 1/3rd of x and 150% of y = \(\displaystyle \frac{x}{3}\times \frac{3}{2}y=\frac{{xy}}{2}\)
Required answer = \(\displaystyle \frac{{xy}}{{2\times xy}}\times 100=50\%\)
(or)
if xy is original number, then \(\displaystyle \frac{{xy}}{2}\) is half or 50% of xy
59. Akbar salary increases every year by 10% in June. If there is no other increase or reduction in the salary and his salary in June 2022 was ₹22,385, what was his salary in June 2020?
(a) ₹18,650
(b) ₹18,000
(c) ₹19,250
(d) ₹18,500
(e) None of these
Solution: (d)
Salary in June 2022 = 22385
Using compound interest
\(\displaystyle A=P\mathop{{\left( {1+\frac{r}{{100}}} \right)}}^{n}\)
\(\displaystyle 22385=P\mathop{{\left( {1+\frac{{10}}{{100}}} \right)}}^{2}\)
\(\displaystyle 22385=P\mathop{{\left( {1+0.1} \right)}}^{2}\)
\(\displaystyle 22385=P\mathop{{\left( {1.1} \right)}}^{2}\)
\(\displaystyle P=\frac{{22385}}{{\mathop{{\left( {1.1} \right)}}^{2}}}\)
\(\displaystyle P=18500\)
Hence his salary in 2020 is ₹18,500
(or)
Alternate direct method,
Salary in June 2020 = \(\displaystyle \frac{{22385}}{{1.1\times 1.1}}=18500\)
60. An HR Company employees 4800 people, out of which 45 percent are males and 60 percent of the males are either 25 years or older. How many males are employed in that HR Company who are younger than 25 years?
(a) 2640
(b) 2160
(c) 1296
(d) 864
(e) None of these
Solution: (d)
Total Number of employees = 4800
45% of these 4800 are male
Therefore, total male = \(\displaystyle \frac{{45}}{{100}}\times 4800=2160\)
60% of these 2160 are 25years or older
Therefore, total male who are 25 years or older=\(\displaystyle \frac{{60}}{{100}}\times 2160=1296\)
The number of males less that 25 years=2160 – 1296 = 864
(or)
Direct alternate method,
Required number = \(\displaystyle 4800\times \frac{{45}}{{100}}\times \frac{{40}}{{100}}=864\)
