Q: The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity?
Solution: Suppose commodity X wil cost 40 paise more than Y after Z years. Then,
(4.20 + 0.40Z) - (6.30 + 0.15Z) = 0.40
=> 0.25Z = 0.40 + 2.10 => Z= 2.50/0.25 = 10
Therefore, X will cost 40 paise more than Y 10 years after 2001 . i.e in 2011Q: When 52416 divided by 312 , the quotient is 168. What will be the quotient when 52.416 is divided by 0.0168 ?
Solution: Given, 52416 / 312 = 168. <=> 52416 / 168 = 312. 52.416 / 0.0168 = 524160 / 168 = 3120.
Q: Karthik read 613 th of a book in 1st week and 59 th of the remaining book in 2nd week. If there were 100 pages unread after 2nd week, how many pages were there in the book ?
Solution: Let the total book be 1 Then, in the 1st week 613th of book is read i.e remaining pages = 1-613=713 in 2nd week he read 59th of it i.e 59×713=35117Remaining pages after 2nd week = 713-35117=28117 But given remaining pages after 2nd week = 100 28x117=100 --> x = 418 The total pages in the book are 418
Q: Karthik is now 32 years old and his son is 7 years old. In how many years will Karthik be twice as old as the son?
Solution: Given Karthik’s age = 32 years Karthik’s son age = 7 years Difference between their ages = K - S = 32 - 7 = 25 years ….(1) Now, required K = 2S ……(2) Put (2) in (1) 2S - S = 25 => S = 25 years Hence, at the age of 25 years of Karthik’s son, Karthik will be twice as his son’s age. 25 - 7 = 18 years Therefore, after 18 years the father be twice as old as the son.
Q: The difference of two numbers is 14. Their LCM and HCF are 441 and 7. Find the two numbers ?
Solution: Since their HCFs are 7, numbers are divisible by 7 and are of the form 7x and 7y Difference = 14 => 7x - 7y = 14=> x - y = 2 product of numbers = product of their hcf and lcm=> 7x * 7y = 441 * 7=> x * y = 63 Now, we havex * y = 63 , x - y = 2=> x = 9 , y = 7 The numbers are 7x and 7y=> 63 and 49
Q: The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
Solution: L.C.M. of 5, 6, 7, 8 = 840. Required number is of the form 840k + 3 Least value of k for which (840k + 3) is divisible by 9 is k = 2. Required number = (840 x 2 + 3) = 1683.
Q: The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
Solution: Required number of students = H.C.F of 1001 and 910 = 91
Q: Meghana alone would take 32 hours more to complete a job than both Meghana and Ganesh together. If Ganesh worked alone, he took 12 1/2 hours more to complete it than both Meghana and Ganesh worked together. What time would they take if both Meghana and Ganesh worked together?
Solution: Time taken by both Meghana and Ganesh to work together is given by = t1 x t2 Where t1 = 32 hrst2 = 12 12 hrs = 252 hrs Therefore, time took by both to work together = 32 x 252 = 16 x 25 = 4 x 5 = 20 hrs
Q: A can do a piece of work in 15 days and B can do it in 16 days and C can do it 24 days. They started the work together and A leaves after 3 days and B leaves after 4 days from the beginning. How long will work lost ?
Solution: 3/15 + 4/16 + x/24 = 1 ⇒x=1315
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