A man eats 3 loaves in 2 days and his wife 2 loaves in 3 days. How long would 26 loaves last for both of them?
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Solution
LCM of 2 and 3 is 6
∴ In 6 days, man eats 9 and his wife eats 4 loaves.
∴ 13 loaves in 6 days and 26 loaves in 12 days
Four terms are in A.P. such that their sum is 120 and greatest among them is 3 times the least. Find the second term.
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Solution
Let a - 3d, a - d, a + d and a + 3d be the four terms.
∴ Adding them 4a = 120 ∴ a = 30
∴ (30 - 3d) × 3 = 30 + 3d
∴ 90 - 9d = 30 + 3d
∴ 60 = 12d ., d = 5
Second term = a - d = 30 -5 = 25
If Harry can walk to a place in 43⁄4 hours, walking at 31⁄4 kmph. How long would it take Lira walking at 31⁄6 kmph. to walk there and back?
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Solution
DIstance traveled by Harry = \(\frac{19}{4}\times \frac{13}{4}\) kms.
Lira covers this distance twice, to and fro.
Time taken by Lira = \(\frac{\frac{19}{4}\times \frac{13}{4}\times 2}{\frac{19}{6}}\)
\(\frac{19}{4}\times \frac{13}{4}\times \frac{2}{1}\times \frac{6}{19}=9\)hours 45 mins.
A barrel contains 36 gallons of beer at 12 noon. One tap draws a pint in every 4 minutes and another draws a quart every 6 minutes. How many pints of beer will be left in the barrel at 12 min. past 8 p.m.?
* 4 quarts = 8 pints = 1 gallon.
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Solution
Capacity of barrel = 36 × 8 = 288 pints. Total time upto 8.12 p.m. is 492 mins.
Beer removed by 1st tap = \(\frac{492}{4}\) = 123 pints.
Beer removed by 2nd tap in 492 mins.
= 2⁄6 x 492 = 164 pints.
Total beer removed = 287 pints.
∴ Quantity of beer left in the barrel is 288 - 287 = 1 pint.
What number must be subtracted from each of the nos. 14, 17,21 so that the results are in G.P.
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Solution
Let x be the no. to be subtracted then 14 - x, 17 - x and 21 - x are in G.P.
∴ (17 - x)2 = (14 - x)(21 - x)
289 + x2 - 34x = x2 + 294 - 14x - 21x
∴ x = 5
OD and OB are bisector of ∠COE and ∠AOC respectively. Find ∠EOD .
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Solution
Let ∠AOB = x, ∠COD = Y
∴ x + x + y + y = 180
∴ x + y = 90
∴ ∠BOC + ∠COD = x + y = 90
If total, sales for business in a certain year wear $18,000. What were sales in August, if August sales were 1/3 the monthly average?
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Solution
Monthly average = \(\frac{18000}{12}\) = 1500
∴ August sales = \(\frac{1500}{3}\) = 500
If (p – q) is 6 more than (x + y) and (p + q) is 3 less than (x – y), then (p – x) =
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Solution
∴ p + q = x - y - 3 .... (I)
p - q = x + y + 6 ....(II)
Adding I and II
2p - 2x = 3
∴ p-x = 1.5
If A = 1 + 1⁄2 + 1⁄4 + 1⁄8 + \(\frac{1}{16}\) B = 1 + A⁄2 The B exceeds A by
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Solution
B = 1 + A⁄2
\(B = 1+\frac{1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}}{2}\)
= 1 + 1⁄2 + 1⁄4 + 1⁄8 + \(\frac{1}{16}\: +\: \frac{1}{32}\)
∴ Difference in B and A is only \(\frac{1}{32}\)
George finishes a work alone in certain number of days. He gets two assistants Harry and Sally, who work 3/4 as fast as he does. If all the three work together, then in what fraction of time would they finish when compared to George working alone?
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Solution
Capacity of G is x per day.
∴ Capacity of Hand S each 0.75x
Combined capacity of G, Hand S will be
x + 0.75x + 0.75x = 2.5x = 5⁄2x.
Time required will be inverse of capacity i.e.2⁄5