Simplification
- A man had 170 currency notes in all, some of which were of ₹ 100 denominations and some of ₹ 50 denominations. The total amount of all these currency notes was ₹ 10000. How much amount did he have in the denominations of ₹ 50 ?
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Hint 1 :
Let the number of ₹ 50 notes = x, then the number of ₹ 100 notes = (170 - x)
According to question.
50x + 100(170 - x) = 10000
Solve the equation.
Hint 2 :
Let the number of ₹ 50 notes = x and the number of ₹ 100 notes = y.
according to given question,
x + y = 170 .............(1)
50x + 170y = 10000............(2)
Solve the equation (1) and (2).Correct Option: C
Solution 1 :
Let the number of ₹ 50 notes = x, then the number of ₹ 100 notes = (170 - x)
According to question.
50x + 100(170 - x) = 10000
divide by 50 the above equation, we will get
⇒ x + 2(170 - x) = 200
⇒ x + 340 - 2x = 200
⇒ -x = 200 - 340 = -140
⇒ x = 140
∴ Required amount ₹ 50 x 140
= ₹ 7000
Solution 2 :
Let the number of ₹ 50 notes = x and the number of ₹ 100 notes = y.
according to given question,
x + y = 170 .............(1)
50x + 100y = 10000............(2)
Divide the equation (2) by 10 , we will get
5x + 17y = 1000............(3)
Multiply the equation (1) by 5
5x + 5y = 850 ------------(4)
Subtract the (4) equation from (3) equation, we will get,
5x +10y - ( 5x + 5y ) = 1000 - 850
⇒ 5x +10y - 5x - 5y = 1000 - 850
⇒ 10y - 5y = 1000 - 850
⇒ 5y = 150
⇒ y = 150/5
⇒ y = 30
Number of ₹ 100 notes = y = 30;
since x + Y = 170
therefore x = 170 - y
⇒ x = 170 - 30
⇒ x = 140
Number of ₹ 50 notes = x = 140
- Mr. Sahni employed a worker for a certain work to be done in some days. He pays ₹20 to the worker for each working day and the payment is reduced by ₹ 3 for each non-working day of the worker. For how many days the worker does remain absent from work if at the end of 120 days, he gets ₹ 560 as total remuneration ?
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Let the worker remains absent for x days.
Then, his working days will be = (120 - x) days.
According to the question,
20 x Working day - 3 x Absent day = 560 ;Correct Option: A
Let the worker remains absent for x days.
Then, his working days = (120 - x) days.
According to the question,
20 x Working day - 3 x Absent day = 560
20(120 - x) - 3x = 560
⇒ 2400 - 20x - 3x = 560
⇒ x = 2400 - 560/23 = 1840/23
= 80 days
- A fruit seller has a crate of apple containing 1 bruised apple for every 40 apples in the crate, If 3 out of every 4 bruised apples are considered unsaleable and there are 9 unsaleable apples in the crate, then how many apples are there in the crate ?
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Let total number of apples in the crate = a
Then, number of bruised apples = a/40 .
Number of unsaleable apples
since 4 bruise apples containing 3 unsaleable apples.
therefore 1 bruise apples will contain 3/4 unsaleable apples
hence a/40 bruise apples will contain 3/4 x a/40 unsaleable apples
= 3/4 x a/40 = 3a/160Correct Option: D
Let total number of apples in the crate = a
Then, number of bruised apples = a/40 .
Number of unsaleable apples
since 4 bruise apples containing 3 unsaleable apples.
therefore 1 bruise apples will contain 3/4 unsaleable apples
hence a/40 bruise apples will contain 3/4 x a/40 unsaleable apples
= 3/4 x a/40 = 3a/160
According to the question.
3a/160 = 9
⇒ a = 9 x 160/3
a = 3 x 160 = 480
- City A has a population of 136000 which is decreasing at the rate of 2400 per year , City B has a population of 84000 which is increasing at the rate of 1600 per year . In how many years will the population of two cities become equal ?
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Let population of cities A and B become equal after x year.
According to the question.
Population of city A = Population of city B
Then,
136000 - 2400x = 84000 + 1600x.Correct Option: C
Let population of cities A and B become equal after x year.
According to the question.
Population of city A = Population of city B
Then,
136000 - 2400 x = 84000 + 1600 x.
⇒ 4000x = 52000
∴ x = 52/4 = 13 year
- 5 - [3/4 +{21/2 - (1/2 + 1/6 - 1/7 )}]/2 = ?
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? = 5 - [3/4 + {5/2 - (1/2 + 1/6 - 1/7)}]/2
= 5 - [3/4 + {5/2 - (1/2 + 7 - 6/42 )}]/2
= 5 - [3/4 + {5/2 - (1/2 + 1/42)}]/2
= 5 - [3/4 + {5/2 - (21 + 1/42)}]/2
= 5 - [3/4 + {5/2 - 22/42)}]/2
= 5 - [3/4 + {105 - 22/42)}]/2
= 5 - [3/4 + 83/42]/2 = 5 - [63 + 166/84]/2
= 5 - 229/84/2 = 420 - 229/84/2 = 191/84/2
= 191/84 x 2 = 191/168 = 123/168Correct Option: A
? = 5 - [3/4 + {5/2 - (1/2 + 1/6 - 1/7)}]/2
= 5 - [3/4 + {5/2 - (1/2 + 7 - 6/42 )}]/2
= 5 - [3/4 + {5/2 - (1/2 + 1/42)}]/2
= 5 - [3/4 + {5/2 - (21 + 1/42)}]/2
= 5 - [3/4 + {5/2 - 22/42)}]/2
= 5 - [3/4 + {105 - 22/42)}]/2
= 5 - [3/4 + 83/42]/2 = 5 - [63 + 166/84]/2
= 5 - 229/84/2 = 420 - 229/84/2 = 191/84/2
= 191/84 x 2 = 191/168 = 123/168
