The length of one diagonal of a rhombus is 80% of the other diagonal. The area of the rhombus is how many times the square of the length of the longer diagonal?
Let length of the longer diagonal = x cm
Then, length of other diagonal
= ( 80/100 x) cm = ( 4/5 x) cm
Area of rhombus = 1/2 x x 4/5 x = 2/5 x^{2}
= 2/5 x (Square of the length of longer diagonal)
On what dates of April, 1995 did Sunday fall?
1993 complete years = 1600 + 300 + 93
= 1600 + 300 + 23 leap years + 70 ordinary yrs.
= (0 + 1 + 23 x 2 + 70) odd days
= 117 odd days
= 16 weeks + 5 odd days
Hence Jan 1, 1994 was a Friday, Jan, February, March have 3, 0 and 3 odd days respectively, or 6 odd days.
Hence, April 1, is a Thursday. April 4 is a sunday Option (c) is correct.
Put x + 1/x = y
The value of the expression
3 π^{c}/ 4 =
Study the following diagram :
The value of (x + y) is
56 = 8 x 7
x = 6x7= 42
∴ y = 8 x 42 = 336
∴ x + y = 336 + 42 = 378
select the correct combination of mathematical signs to replace * sign to balance the given equation.
24*3*2*12*3
A number, when 40 is added to it,increases to its 120%. What is threefourth of that number?
x + 40 = 120/100 x
⇒ 100x + 4000 = 120x
⇒ 20x = 4000
⇒ x = 200
and 3/4 x 200 = 150
A garment company declared 15% discount for wholesale buyers. Mr Sachdev bought garments from the company for Rs 25000 after getting discount. He fixed up the selling price of garments in such a way that he earned a profit of 8 % on original company price. What is approximate total selling price?
Cost price of garments = Rs 25000
Original company price = 25000/85 x 100
∴ Selling price of garments
= 25000/85 x 100 x 108/100
= Rs 31764.71 ≈ Rs 31000
100 × 10  100 + 2000 ÷ 100 = ?
100 × 10  100 + 2000 ÷ 100
= 100 (10  1) + 20
= 900 + 20 = 920
Shyam went from Delhi to Shimla via Chandigarh by car. The distance from Delhi to Chandigarh is (3/4) times the distance from Chandigarh to Shimla. The average speed from Delhi to Chandigarh was half as much as that from Chandigarh to Shimla. If the average speed for the entire journey was 49 km/hr, what was the average speed from Chandigarh to Shimla?
The ratio of the distances between (DelhiChandigarh) : (ChandigarhShimla) = 3 : 4.
The ratio of the speeds between (DelhiChandigarh) : (ChandigarhShimla) = 3 : 2.
Let the distances be 3x & 4x respectively and speeds be 3y and 2y.
So the time taken will be ( x/y ) and ( 2x/y ) respectively
Since average speed is given as (Total Distance) (Total Time) = (7x) x/y + 2x/y = 7y/3 = 49. Hence y = 21
So the average speed from Chandigarh to Shimla = 2y = 42 kmph.
A jailor decided to play a game with his prisoners who were extremely adept at logical analysis. The prisoners were Aristotle, Bach, Coutin, Dell and Einstein. He gave them each a box of money and said 'Each of you have received a box of currency. All boxes look identical from outside'. The jailor then asked each prisoner to secretly open the boxes and look at the currency inside. He then said 'three of you have a box containing Indian Rupees; two of you have a box containing US Dollars, I shall now give each one of you a chit containing information about the box of exactly one other person'. He did so and asked them to open the chit and see the information provided to them. Jailor again said 'None of you will be able to tell the exact currency of any third person'. Then he announced 'Bach has a box containing Indian Rupees' Aristotle immediately said 'I Know the currency of all 5 people'. After some time Einstein also said 'so do I', now assume: a prisoner speaks up as soon as he is able to deduce the currency of all five prisoners.
Q. A part from Bach, the prisoners with Indian currency were
Aristotle, being the first to deduce after being told about Bach s currency, would have the same currency as the currency of the person whose chit he received. Hence, we can deduce that Bach and Aristotle along with a third person would have Indian rupees, the other two having US Dollars
A jailor decided to play a game with his prisoners who were extremely adept at logical analysis. The prisoners were Aristotle, Bach, Coutin, Dell and Einstein. He gave them each a box of money and said 'Each of you have received a box of currency. All boxes look identical from outside'. The jailor then asked each prisoner to secretly open the boxes and look at the currency inside. He then said 'three of you have a box containing Indian Rupees; two of you have a box containing US Dollars, I shall now give each one of you a chit containing information about the box of exactly one other person'. He did so and asked them to open the chit and see the information provided to them. Jailor again said 'None of you will be able to tell the exact currency of any third person'. Then he announced 'Bach has a box containing Indian Rupees' Aristotle immediately said 'I Know the currency of all 5 people'. After some time Einstein also said 'so do I', now assume: a prisoner speaks up as soon as he is able to deduce the currency of all five prisoners.
Q. The prisoners given US Dollars were
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