41. In a class, number of girls is more than the number of boys by 20% of the total strength. What is the ratio of boys to girls ?
Sol:
Let total number of students = 100
& number of boys = x
∴ number of girls = x + 20% of 100
= x + 20
∴ x + x + 20 = 100
2x = 80
x = 40
∴ boys = 40
& girls = 60
∴ boys : girls = 40 : 60 = 2 : 3 Answer
42. The radius of sphere is 10 cm. Find out its surface area is how % of its volume?
Sol:
\(\frac{{surface\;area}}{{volume}} = \frac{{4\pi {r^2}}}{{\frac{4}{3}\pi {r^3}}} = \frac{3}{r} = \frac{3}{{10}}\)
∴ required % = \(\frac{3}{{10}} \times 100\)% = 30% Answer
43. A fruit seller had some apples. He sells 40% apples and stills has 360 apples. Then how much apples originally he had ?
Sol:
He sells 40% apples. So he will have 60% apples remaining with him.
& given that 60% ⟶ 360
1% ⟶ 6
& originally he has 100% apples which will be equal to 100 × 6 = 600 apples Answer
44. A customer asks for the production of ‘a’ number of goods. The company produces ‘b’ number of goods daily, out of which c% units are for sale. Then in how many days order will be completed ?
Sol:
Units daily produced = b × c% = \(\frac{{bc}}{{100}}\)
total units required = a
units daily ready for sale = b × c%
∴ Number of days required to complete
= \(\frac{a}{{\left( {\frac{{bc}}{{100}}} \right)}}\)
= \( \boldsymbol\frac{{100a}}{{bc}}} \) Answer
45. The sujm of two numbers is 280. If the bigger number is decreased by 54% and the smaller number is increased by 15% then the number obtained are equal. Find the numbers.
Sol:
Let bigger number = x
& smaller number = y
x – x × 54% = y + y × 15% (Given)
⟹ \(\frac{{46x}}{{100}} = \frac{{115y}}{{100}}\)
46. The expences on wheat, Rice and sugar of a familuy are in the ratio 15 : 18 : 7. The price of theser articles are increased by 20%, 30% and 40% respectively. Then find the total increased expense of the family.
Sol:
∴ % inrease = \(\frac{{30 + 54 + 28}}{{150 + 180 + 70}} \times 100\)
= \(\frac{{112}}{{400}} \times 100\)
= 28% Answer
47. Due to an increase of 50% in the price of bananas, 4 bananas less are available for Rs. 24. What will be the present rate of per dozen bananas ?
Sol:
∴ original price = 2 Rs./banana
∴ Number of bananas bought for Rs. 24 = \(\frac{{24}}{2}\) = 12 = 1 dozen
& new price of per dozen banana = 3 × 12 = 36 Rs. Answer
48. 90% of boys in a school passed in Hindi, 50% passed in english and 240 boys passed in both the subjects. If no student failed in both the subjects, then find the total number of boys.
Sol:
Total percentage of boys who passed in either Hindi or English = 90 + 50
= 140%
∴ total boys who passed in both the subjects = 140 – 100 = 40%
Given that,
40% ⟶ 240
∴ 1% ⟶ 60
∴ total number of boys = 100% = 60 × 100 = 600 Answer
49. Ankit spents \( \boldsymbol{33\frac{1}{3}} \) of his salary on the item of daily use and 30% of the remainder on house rent. After that he is left with 1120 Rs. How much is his salary ?
Sol:
50. A man spent 30% of an amount to buy grocery and10% of the remaining to transportation then he donated 90 Rs. If he is left with 1800. What is the amount spent on transport ?
Sol:
∴ amount spent on transport
= 300 × 70% × 10%
= 3000 × \(3000 \times \frac{{70}}{{100}} \times \frac{{10}}{{100}}\)
= 210 Answer