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A father is 3 yrs more than thrice the age of his son. Three yrs later, the father will be 10 yrs more than twice the age of his son. The ratio of their ages is
Let present age of the son = x.
Ten present age of the father = 3x + 3
After three years, age of the son = (x+3) and age of the father = (3x+3+3) = (3x+6)
Given that (3x+6) = 10 + 2(x+3)
⇒ 3x + 6 = 10 + 2x + 6
⇒ x = 10
Present age of the father = 3x+3 = 3x10 + 3 = 33
ratio = 33 : 10
The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is :
Average of 5 numbers = 27
∴ Sum of 5 numbers = 27 x 5 = 135
Given one number is excluded and average of remaining 4 numbers = 25
∴ Sum of remaining 4 numbers = 25 x 4 = 100
∴ Excluded Number = 135  100 = 35
The wheel of a scooter has a diameter of 70 cm. The number revolution it must make to maintain a speed of 33 km/hour is
The distance covered by the wheel in one m = 33 x 1000 x 100/60 = 55000
The distance covered by the wheel in one revolution
= The circumference of the wheel = 2πr
= 2 x 22/7 x 70/2 = 220cm
∴ Number of revolutions of the wheel = 55000/220 = 250
A sum of money lent out at simple interests amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is:
Principal + SI for 2 years = Rs 720 ……(I)
Principal + SI for 7 years = Rs 1020 ……(II)
Subtracting equation (I) from (II),
S.I. for 5 years = (1020 – 720) = Rs 300
∴ S.I. for 2 years = 300 x 2/5 = Rs 120
∴ Principal = (720 – 120) = Rs 600
India exchanged the list of nuclear installations and facilities with which country, simultaneously through diplomatic channels?
Let X be any point within a square ABCD. On AX a square AXYZ is described such that D is within it. Which one of the following is correct?
In ΔABX and ΔADZ,
AB = AD (side of a square ABCD)
and AX = AZ (side of a square AXYZ)
Let ∠BAX = θ
∴ ∠XAD = 90^{o}  θ
Also, AXYZ is a square
∴ ∠ZAX = 90^{o}
⇒ ∠ZAD + ∠XAD = 90^{o}
⇒ ∠ZAD = 90^{o}  (90^{o}  θ) = θ
i.e., ∠BAX = ∠ZAD
∴ ΔABX = ΔADZ
∴ BX = DZ (by CPCT)
A survey was conducted on a samples of 1000 persons with reference to their knowledge of English, French and German. The result of the survey are presented in the given Venn diagram. The ratio of the number of the persons who do not know any of the three languages to those who know all the three languages, is
No. of people who do not know any of the three languages
= 1000  (170 + 105 + 180 + 175 + 85 + 78 + 200)
= 1000  993 = 7
∴ Required ratio = 7/175 = 1/25
If 'x' means '+', '+' means '÷', '÷' means '' and '' means 'x', what will be the value of the following expression?
5  7 x 9 + 3 ÷ 2
5  7 x 9 + 3 ÷ 2
⇒ 5 x 7 + 9 ÷ 3  2 = 35 + 3  2
⇒ 38  2 = 36
Milk and water are in the ratio of 3:2 in a mixture of 80 litres. How much water should be added so that the ratio of the milk and water becomes 2:3?
Quantity of milk = (80 x 3/5 ) = 48 liters
Quantity of water in it = 80  48 = 32 liters
New ratio = 2 : 3
Let quantity of water to be added further be x litres
Then milk : water = 48/32 + x
Now, 48 /32 + x = 2/3
⇒ 64 + 2x = 144
⇒ 2x = 144  64 = 80⇒ x = 80/2 = 40
If (28)^{3} is subtracted from the square of a number, the answer so obtained is 1457. What is the number ?
Let the number be x
According to the question,
x^{2}  (28)^{3} = 1457
⇒ x^{2}  21952 = 1457
⇒ x^{2}  21952  1457 = 0
⇒ x^{2} = 23409
⇒ x = √ 23409 = 153
M, P and Q jointly thought of engaging themselves in a business venture. It was agreed that M would invest Rs 6500 for 6 months, P Rs 8400 for 5 months and Q Rs 10,000 for 3 months. M was to be the working member of the group for which he was to receives 5% of the profits. The profit earned was Rs 7030.Calculate the share of Q in the profit.
M, P, Q share the remaining profit of Rs 7,030 in the ratio 6500 x 6 : 8400 x 5 : 10000 x 3
i.e., 13 : 14 : 10
∴ Q's share = 14/37 x 7030 = Rs 2,660
A and B together can do a piece of work in 12 days. B and C together can do the same work in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days will C alone be able to do the work?
Word done by (A + B) in 1 day = 1/12
Work done by (B + C) in 1 day = 1/16
Let C does a work in x days
Then work done by C in 1 day = 1/x
Given A's 5 day's work + B's 7 day's work + C's 13 day's work = 1
Or (A + B)'s 5 day's (B + C)'s 2 day's + C's 11 day's
5/12 + 2/16 + 11/x = 1
⇒ x = 24 days
If 2y cosθ=x sinθ and 2x secθy cosecθ=3, then x^{2}+4y^{2}=
What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
Each of the following questions consists of two sets of figures. Figures 1,2,3 and 4 constitute the Problem Set while figures A,B,C,D and E constitute the Answer Set. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the Answer Set .
In the following problems, out of the five figures marked 1, 2, 3, 4, and 5, four are similar in a certain manner. However one figure is not like the other four. Choose the figure which is different from the rest.
Only in fig. (3), two of the four elements are oriented in the same direction.
Hence, fig. (3) is the answer.
In the following questions, select a figure from amongst the four alternatives, which when placed in the blank space of fig. (X) would complete the pattern.
Eight friends A, B, C, D, E, F, G and H are sitting around a circle facing the centre. H is to the immediate left of E who is third to the right of B. C is second to the right of D and is not a neighbour of B. F is second to the right of G and is not a neighbour of C.
Q. Who is second to the right of E?
Find out from amongst the four alternatives as to how the pattern would appear when the transparent sheet is folded at the dotted line.
Answer these question based on the table given below .
The Hotel Company of India (HCI) owns seven Hotels with the same capacity. The occupancy rates across the seven hotels are given in the following table.
Q. In which year did HCI witness the highest occupancy rate?
Total occupancy for the year 1999 is the highest
2001 = 416, 2000 = 428,
1999 = 449, 1998 = 446, 1997 = 448
Answer these question based on the table given below .
The Hotel Company of India (HCI) owns seven Hotels with the same capacity. The occupancy rates across the seven hotels are given in the following table.
Q. Which one of the following statements is true?
Answer these question based on the table given below .
The Hotel Company of India (HCI) owns seven Hotels with the same capacity. The occupancy rates across the seven hotels are given in the following table.
Q. Which of the following statement (s) is/are false?
Average occupancy rate hotel wise is given below
From the above table it is given that all the statements given are false
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