There are 48 books on 3 shelves. If 3 books from third shelf are shifted to second, there will be same number of books on first and third shelves and double the number of books on second shelf. How many books were there on three shelves originally?
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Solution
Check with the options.
For a given volume, surface area is least for
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Solution
Sphere has the least surface area.
The front wheel of wagon is 6 ft. and back wheel is 9 ft. in circumference. Find the distance traveled when front wheel has made 20 more revolution than back wheel.
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Solution
LCM of 6 and 9 is 18. If cart travels 18 ft., front wheel makes 3 revolutions and back wheel makes 2 revolutions.
Thus front wheel makes 1 more revolution than Hick wheel in 18 ft.
∴ 20 more revolutions in 360 ft.
A student planned to complete a college term paper on Monday 12th June. The deadline was then postponed and set for 53 days after September 14th. On which day of week was task completed?
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Solution
14th September is 94 days after 12th June. (18 + 31 + 31 + 14)
College term paper will complete 53 days after 14th September.
∴ It will complete 94 + 53 = 147 days = 21
∴ 53 days after 14th September will be again a Monday
Ratio of illiterate male and illiterate female persons in a village is 5 : 3. 60% of illiterate males have enrolled in literacy campaign. What can be the greatest possible proportion of people enrolled for literacy campaign from among illiterate population?
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Solution
Let number of illiterate males be 5x and illiterate female be 3x.
60% of illiterate male i.e. 3x have enrolled for literacy campaign.
To find the greatest possible enrollment, we have to assume that all the illiterate female have joined the campaign. Hence the maximum possible enrollment is 3x male + 3x female = 6x
∴ \(\frac{6x}{8x}\) i.e. 3⁄4 is the ratio.
2 Men start together to walk a certain distance, one at 3 3/4 kmph and other at 3 kmph. The former arrives half an hour before the latter. Find the distance.
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Solution
Let the distance be x kms.
\(\frac{x}{3}-\frac{x}{3\frac{3}{4}}=\frac{1}{2}\) ∴ x = 7.5 kms.
x⁄y = 9⁄5 then \(\frac{x^{2}+y^{2}}{x^{2}-y^{2}}\)=
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Solution
\(\frac{x^{2}}{y^{2}}=\frac{81}{25}\) ∴\(\frac{x^{2}+y^{2}}{x^{2}-y^{2}}=\frac{106}{56}=\frac{53}{28}\)
\(\frac{a}{7}=\frac{b}{3}=\frac{3a -2b}{k}\) Find k
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Solution
a⁄7 = b⁄3 ∴ 3a = 7b
b⁄3 = \(\frac{3a-2b}{k}\) ∴\(\frac{b}{3}=\frac{7b-2b}{k}=\frac{5b}{k}\)
∴ bk = 15b ∴ k = 15
Sum of n terms of an A. P. is given by 2n2 + 5n. Find the fourth term of this A.P.
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Solution
Sum of first 4 terms - Sum of first 3 terms = fourth term.
∴ [2 × (4)2 + 5 × 4]-[2 × (3)2 + 5 × 3]
= (32 + 20) - (18 + 15) = 52 - 33 = 19
In the ancient Chinese puzzle called Tangrams, a sheet in a particular shape is cut into different patterns and all these pieces are rearranged to get some other meaningful shape. In one such version, if a circular sheet of diameter 10.5 em is cut into some patterns and rearranged to form a parallelogram of base 10.5 em what will be the altitude of that parallelogram in cm?
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Solution
Since all the pieces are used in getting a new shape, it implies that the areas of circle and parallelogram are equal.
∴\(\frac{22}{7}\times \frac{10.5}{2}\times \frac{10.5}{2}= 10.5\) × attitude of parallelogram
∴ Altitude = \(\frac{22\times10.5\times10.5}{7\times 4\times 10.5}\)
∴ Altitude =\(\frac{165}{2}\)= 8.25 cm