MISCELLANEOUS QUESTIONS
THERE IS 40% INCREASE IN AN AMOUNT IN 8 YEARS AT SIMPLE INTEREST. WHAT WILL BE THE COMPOUND INTEREST IN RS OF RS 30000 AFTER 2 YEARS AT THE SAME RATE?
ACCORDING TO THE QUESTION,
IF THE PRINCIPLE = RS 100
THEN INTEREST = RS 40
THEREFORE RATE = ( I * 100 ) / ( P * T )
= 40 * 100 * 1/100 * 1/8
= 5 % p. a.
CASE II,
A = P[1+R/100]^T
A = 30000[1+5/100]^2
A = 30000[1+1/20]^2
A = 30000 * 21/20 * 21/20
A = RS 33075
THEREFORE,
= RS [33075 - 30000]
= RS 3075
WHAT IS THE MEASURE OF THE CENTRAL ANGLE OF THE ARC WHOSE LENGTH IS 11 CM AND RADIUS OF THE CIRCLE IS 14 CM?
ARC LENGTH IS 11 CM AND IF WE CALCULATE THE CIRCUMFERENCE OF THE CIRCLE,
= 2 * pi * r
= 2 * 22/7 * 14
= 88 cm
AND NOW WE HAVE TO FIND THE ANGLE OF THE ARC,
WE KNOW THAT IN A CIRCLE THE ANGLE IN THE MIDDLE IS 360 deg
SO,
88cm = 360 deg
1 cm = 360 / 88
AND IN ARC WHICH IS 11 cm,
11 cm = 360/88 * 11
= 45 deg
IF THE SHOPKEEPER SELLS AN ITEM AT RS 960 WHICH IS MARKED AS RS 1200, WHAT IS THE DISCOUNT HE IS OFFERING?
DISCOUNT = RS [1200 - 960] = RS 240
IF THE RATE OF THE DISCOUNT IN %, THEN
x% OF 1200 = 240
x * 1200/100 = 240
x = 240/12
x = 20%
A DISHONEST DEALER PROFESSES TO SELL HIS GOODS AT THE COST PRICE BUT USES A FALSE WEIGHT OF 850g INSTEAD OF 1kg. HIS GAIN PERCENT IS,
PROFIT PERCENT = 150 / [1000 - 150] * 100
150 * 100 * 1/850 = 300/17
= CHANGE IT INTO MIXED FRACTION IF THE ANSWER IS IN MIXED FRACTION
A TRAIN 150 METRES LONG CROSSES A MILESTONE IN 15 SECONDS AND CROSSES ANOTHER TRAIN OF THE SAME LENGTH TRAVELLING IN THE OPPOSITE DIRECTION IN 12 SECONDS. THE SPEED OF THE SECOND TRAIN IN KM/HR IS,
SPEED OF THE TRAIN = 150/50 = 10 m/sec
CASE II,
TIME = LENGTH OF THE BOTH TRAINS / RELATIVE SPEED
12 = 2 * 150 * 1/[10+x]
CROSS MULTIPLY THEM,
120 + 12x = 2 * 150
120 + 12x = 300
12x = 300 - 120
12x = 180
x = 180/12
x = 15 m/sec
BUT YOU HAVE TO FIND THE ANSWER IN km/hr
MULTIPLY IT WITH 18/5
=15 * 18 * 1/5
=54 km/hr
ACCORDING TO THE QUESTION,
IF THE PRINCIPLE = RS 100
THEN INTEREST = RS 40
THEREFORE RATE = ( I * 100 ) / ( P * T )
= 40 * 100 * 1/100 * 1/8
= 5 % p. a.
CASE II,
A = P[1+R/100]^T
A = 30000[1+5/100]^2
A = 30000[1+1/20]^2
A = 30000 * 21/20 * 21/20
A = RS 33075
THEREFORE,
= RS [33075 - 30000]
= RS 3075
WHAT IS THE MEASURE OF THE CENTRAL ANGLE OF THE ARC WHOSE LENGTH IS 11 CM AND RADIUS OF THE CIRCLE IS 14 CM?
ARC LENGTH IS 11 CM AND IF WE CALCULATE THE CIRCUMFERENCE OF THE CIRCLE,
= 2 * pi * r
= 2 * 22/7 * 14
= 88 cm
AND NOW WE HAVE TO FIND THE ANGLE OF THE ARC,
WE KNOW THAT IN A CIRCLE THE ANGLE IN THE MIDDLE IS 360 deg
SO,
88cm = 360 deg
1 cm = 360 / 88
AND IN ARC WHICH IS 11 cm,
11 cm = 360/88 * 11
= 45 deg
IF THE SHOPKEEPER SELLS AN ITEM AT RS 960 WHICH IS MARKED AS RS 1200, WHAT IS THE DISCOUNT HE IS OFFERING?
DISCOUNT = RS [1200 - 960] = RS 240
IF THE RATE OF THE DISCOUNT IN %, THEN
x% OF 1200 = 240
x * 1200/100 = 240
x = 240/12
x = 20%
A DISHONEST DEALER PROFESSES TO SELL HIS GOODS AT THE COST PRICE BUT USES A FALSE WEIGHT OF 850g INSTEAD OF 1kg. HIS GAIN PERCENT IS,
PROFIT PERCENT = 150 / [1000 - 150] * 100
150 * 100 * 1/850 = 300/17
= CHANGE IT INTO MIXED FRACTION IF THE ANSWER IS IN MIXED FRACTION
A TRAIN 150 METRES LONG CROSSES A MILESTONE IN 15 SECONDS AND CROSSES ANOTHER TRAIN OF THE SAME LENGTH TRAVELLING IN THE OPPOSITE DIRECTION IN 12 SECONDS. THE SPEED OF THE SECOND TRAIN IN KM/HR IS,
SPEED OF THE TRAIN = 150/50 = 10 m/sec
CASE II,
TIME = LENGTH OF THE BOTH TRAINS / RELATIVE SPEED
12 = 2 * 150 * 1/[10+x]
CROSS MULTIPLY THEM,
120 + 12x = 2 * 150
120 + 12x = 300
12x = 300 - 120
12x = 180
x = 180/12
x = 15 m/sec
BUT YOU HAVE TO FIND THE ANSWER IN km/hr
MULTIPLY IT WITH 18/5
=15 * 18 * 1/5
=54 km/hr
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