Try yourself:The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. If Kamala's income goes down by 4% and Bimala's goes up by 10%, then the percentage by which Kamala's income would exceed Bimala's is nearest to
[2019]
Explanation
Let Bimala's income be B. Amala's income is 20% more than B. So, A = 1.2 B Similarly, Amala's income is 20% less than that of Kamala. A = 0.8K Therefore, 1.2B = 0.8K (or) K = (3/2)B Now, Bimala's new income goes up by 10% = 1.1B Kamala's income goes down by 4% 4% (1.5B) = 0.06B Therefore, Kamala's new income is = 1.5B - 0.06B = 1.44B So, K = 1.44B and B = 1.1 B Percentage change = 0.34 B = (0.34/1.1) x 100 = 31%
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Try yourself:Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed for passing the examination is
[2019]
Explanation
Meena scores 40 % in an exam After review, she scores 50 % more ⇒ Increase of 50 % from 40 % = 40% + 20% = 60% She fails by 35 marks, by scoring 60% 60% score = Pass mark - 35 ... (1) If her post review score is increased by 20%, she would have 7 more than the pass mark. 20% of 60% = 12 % So, 60% + 12% = 72% of marks = Pass mark + 7 ...(2) So, 12% marks = 35 + 7 (5: 1 ratio) So, similarly 12% can be re written as 10 % and 2 % (maintaining the 5:1 ratio) Hence the pass percentage = 60 % + 10 % = 70% (or) Pass percentage = 72 % - 2 % = 70%
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Try yourself:In a class, 60% of the students are girls and the rest are boys. There are 30 more girls than boys. If 68% of the students, including 30 boys,pass an examination, the percentage of the girls who do not pass is
[TITA 2019]
Correct Answer : 20
Explanation
Given that there are 60 % girls and 40 % boys It is also given that there are 30 more girls than boys. So, (60 % - 40 %) of total class strength = 30 students ⇒ 20 % of total class strength = 30 students ⇒ Total class strength = 30 x 5 = 150 students It is also given that 68% of students pass the the examination, which includes 30 boys So, Number of students passed = 68% of Total students ⇒ Number of students passed = (68/100) x 150 = 102 students ⇒ Since the number of boys passed is 30, ⇒ Number of girls passed = 102 - 30 = 72 Total number of girls = (60/100) x 150 =90 Total number of girls = Girls who passed + Girls who did not pass Girls who did not pass = 90 - 72 = 18 Percentage of girls who did not pass = (18/90) x 100 = 20%
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Try yourself:In 2010, a library contained a total of 11500 books in two categories - fiction and non-fiction. In 2015, the library contained a total of 12760 books in these two categories. During this period, there was 10% increase in the fiction category while there was 12% increase in the non-fiction category. How many fiction books were in the library in 2015?
[2019]
Explanation
Increase in books = 12760 - 11500 = 1260 + x (11500 - x) = 1260 10x + 12 x 11500 - 12x = 126000 x = 6000 books So, Fiction books in 2015, 6000 + 600 = 6600 books
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*Answer can only contain numeric values
Try yourself:In an examination, the score of A was 10% less than that of B, the score of B was 25% more than that of C, and the score of C was 20% less than that of D. If A scored 72, then the score of D was
[TITA 2019]
Correct Answer : 80
Explanation
From the data, A scored 72 A's score was 10% less than B So, Score of B = 80 We know that B was 25% more than C So, C x (5/4) = 80 C = 64 Now, we know that D scored 20% less than D So, C = (4/5) x D 64 = (4/5) x D D = 80 marks
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Try yourself:In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks, but falls short of the pass mark by 68%. Which one of the following is then correct?
[2018]
Explanation
Given Max. mark = N and Pass mark = 45% of N A scores 36 marks and falls short of the pass mark by 68% This means the pass mark must be reduced by (100 - 68)% = 32% So, A scored 32% (45% N) = 36 N = 250 marks The only option whose range falls within the obtained value is (B) 243 ≤ N ≤ 252
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*Answer can only contain numeric values
Try yourself:Arun's present age in years is 40% of Barun's. In another few years, Arun's age will be half of Barun's. By what percentage will Barun's age increase during this period?
[TITA 2017]
Correct Answer : 20
Explanation
Given that Arun's present age in years is 40% of Barun's. And after few years, Arun’s age will be half of Barun’s. We have to find by what percentage will Barun’s age increase during this period. So Arun’s present age is 2x and Barun’s present age will be equal to 5x. 2(2x + y) = 5x + y 4x + 2y = 5x + y 4x + 2y = 5x + y y = x So 2x and 5x becomes 3x and 6x respectively. By what percentage will Barun's age increase during this period is that x increases of 5x so it increases by 20%. Hence 20% of Barun’s age will increase during this period.
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*Answer can only contain numeric values
Try yourself:Ravi invests 50% of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi's savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs 59500, then Ravi's total monthly savings (in Rs) is:
[TITA 2017]
Correct Answer : 70000
Explanation
Ravi invests 50% of his monthly savings in fixed deposits i.e from the remaining 50%, 30% percent of the rest of his savings = 15% is invested in stocks. And the rest i.e 50 – 15 = 35% goes into Ravi's savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs 59500 i.e. 50 + 35 = 85 % ⇒ 85% of total savings = 59500 We have to find the Ravi's total monthly savings (in Rs) ⇒ Total savings = Ravi's total monthly savings is 70000 Rupees.
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Try yourself:The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is:
[2017]
Explanation
Given that the number of girls appearing for an admission test is twice the number of boys. Let x be the number of boys and 2x be the number of girls. We have to find the % of candidates who do not get admission if 30% of the girls and 45% of the boys get admission. Those who got admission is 1.05x and those who do not get admission is 1.95x. So, The percentage of candidates who do not get admission is 65%.
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Try yourself:Out of the shirts produced in a factory, 15% are defective, while 20% of the rest are sold in the domestic market. If the remaining 8840 shirts are left for export, then the number of shirts produced in the factory is
[2017]
Explanation
Given that in a shirt factory , 15% of the shirts produced are defective so 85% are non defective. From this remaining 85% non defective shirts, 20% are sold in domestic market and the remaining 80% are left for export which is equal to 8840 shirts i.e. 80% of 85% of x = 8840 ⇒ x = 13000 The number of shirts produced in the factory is 13000
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Try yourself:In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to
[2017]
Explanation
Given that the production of food grains increased by 40%. Let initial production be y and after increase it becomes 1.4x Per capita production of food grains increased by 27%. Per capita income = ⇒ let the initial Per capita income be (x/y). After increase it becomes 1.27[x/y]. Hence there is an increase of 10% in the population of the village.
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x (11500 - x) = 1260
