Two taps can fill a cistern in 4 hours and 16 hours, respectively. A
third tap can empty it in 4 hours. How long (in hours) will it take to
fill one-fourth of the empty cistern if all the taps are opened
together?
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Simplify: 30 + [{-9 × (26 - 13 + 5)}]
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The price of fuel decreases by 55%, 35% and 45% in three successive
months, but increases by 40% in the fourth month. What is the
percentage decrease in the price of fuel in the fourth month as
compared to its original price? (Round off to 2 decimal places.)
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A shirt's price is decreased from ₹200 to ₹180. What is the
percentage decrease?
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The fourth proportional to 4, 6, and 8 is m. The third proportional to
8 and m is n. What is the value of n?
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A shopkeeper marks a jacket at ₹2,000. He gives a 20% discount, but
charges 5% GST on the discounted price. What is the final price the
customer pays?
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Evaluate 22 3 + (-15) 3 + (-7) 3
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A regular octagonal fountain has a circumradius of 10 m. Find the
approximate length of each side.
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If the height at which a ladder touches the wall is the mean
proportional between 6 meters and 24 meters, at what height does
the ladder touch the wall?
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A sum of ₹2000 is invested at 20% compound interest per annum,
compounded annually for 2 years. What is the compound interest
earned at the end of 2 years?
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A can complete a job in 9 days, while each of B and C can complete it
in 18 days. All three start working together and work for x days.
Then A leaves, and B and C together finish the remaining work in x
days. Find the value of x.
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What is the third proportional to 0.25 and 0.15?
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The arithmetic mean of 25 observations is 32.6. If the arithmetic
mean of the first 24 observations is 30, what is the 25 th observation?
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A motorist travels a certain journey in two stages. In the first stage,
he travels for one-third of the total time at 30 km/hr. In the second
stage, he travels for the rest of the time at 60 km/hr. He returns to
the start at a uniform speed of 75 km/hr. What is the average speed
for the entire round trip?
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The H.C.F. and L.C.M. of two numbers are 25 and 500, respectively. If
the first number is divided by 2, the quotient is 50 and the
remainder is zero. Find the second number.
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What sum (in ₹) will earn a simple interest of ₹1,440 in 2 years at
12% per year rate of interest?
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The present age of Amit is twice that of his brother Sumit. Five years
ago, the ratio of their ages was 5:2. What is Sumit's present age?
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An amount of ₹120 is paid using ₹10, ₹5 and ₹2 coins. If the number
of coins of ₹10 and ₹2 are interchanged, then the amount becomes
₹304. If the number of ₹5 and ₹2 coins are interchanged, then the
amount is ₹165. How many ₹2 coins are used in the payment of
₹120?
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A shopkeeper marks an article at 40% above the cost price and
allows a discount of 25%. What is the percentage profit or loss?
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A bus travels at a uniform speed of 54 km/hr. How many meters
does it cover in 1 minute?
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Five friends participated in a cooking contest and scored 6, 8, 7, 9,
and 5 out of 10, respectively. What is the arithmetic mean of their
scores?
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A shopkeeper offers the following schemes on toys of the same
marked price.
(A) Successive discounts of 34% and 37% on any number of toys
bought.
(B) Successive discounts of 36%, 15% and 14% on any number of
toys bought.
(C) 33% discount on the first 6 toys and 9% discount on each toy
thereon.
(D) 3 toys free of cost on buying 9 toys.
A customer wants to buy 9 toys. Which of the above schemes is the
least beneficial to her?
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A dishonest shopkeeper professes to sell his goods at a 35% loss but
uses a false balance and gains 85%. The actual weight (rounded off
to one decimal place) he uses for 1 kg is:
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Three numbers are in the ratio 4 : 3 : 13, and their LCM is 4524. Their
HCF is:8624
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A square is drawn inside another square such that each vertex of the inner
perimeter of the inner square is 40 cm, find the perimeter of the outer square.
d.
D. square lies at the midpoint of a side of the outer square. If the
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