Mr. Sharma left onethird of his property to his daughter, one fourth to his son and the remainder to his wife. If his wife’s share is Rs 18000 what was the worth of Mr. Sharma’s total property?
Let the total property be Rs x.
In an examination, a student requires 40% of the total marks to pass. If Manoj gets 185 marks and fails by 15 marks what is the total marks?
50 kg of an alloy of nickel and iron contains 60% nickel. How much nickel must be melted into it to make the alloy contain 75% of nickel?
Quantity of nickel in 50 kg of alloy
= 60% of 50 kg = 30 kg
Let the required quantity of lead = x kg
Weight of new alloy = (30 + x ) kg
⇒ 120 + 4x = 150 + 3x
⇒ 4x – 3x = 150 – 120 ⇒
x = 30
The sum of digits of a two digit number is 9. If 27 is added to the number its digits get interchanged. What is the number?
Let unit’s digit be x.
Ten’s digit = (9 – x)
Number = 10(9 – x) + 1× x = 90 –10x + x
∴ 90 – 9x + 27 = x × 10 + (9 – x)1.
⇒ 117 – 9x = 10 x + 9 –x
⇒ 117 – 9x = 9x + 9
A bookseller earned a profit of 5% by selling a book for Rs 714. What is the cost price of the book?
Let the cost price be Rs x.
∴ x + 5% of x = 714
The length of a rectangle is three times of its breadth. Its perimeter is 128m, what is its length?
Let the breadth of rectangle = x
Length = 3x
Perimeter of rectangle = 128
∴ 2(x + 3x) = 128
Ramesh travelled 3/5 of his journey by rail, 1/4 by a car, 1/8 by a bus and the remaining 4 km on foot. What is the length of total journey?
Let the total journey be x km.
A number consists of two–digits whose sum is 8. If 18 is added to the number its digits are reversed. What is that number?
Let the unit’s digit be x.
10’s digit = 8–x.
Number = 10(8–x) + 1×x
= 80 – 10x + x = 80 – 9x
and 80 –9x + 18 = 10 × x + (8–x) 1
⇒ 98 –9x = 10x + 8 –x
⇒ 98 –9x = 9x + 8
Number = 80 – 9×5 = 80 – 45 = 35
A number is as much greater than 21 as it is less than 71. What is that number?
Let the number be x
∴ x – 21 = 71 – x
⇒ x + x = 71 + 21
⇒ 2x = 92
Two supplementary angles differ by 20°. What is the measure of smaller angle?
Let the smaller angle be x.
∴ Other angle = x + 20°
Now x + x + 20° = 180°
⇒ 2x = 160°
⇒ x = 80°
A number when multiplied by 5 is increased by 80. What is that number?
Let the number be x.
∴ 5x = x +80
⇒ 5x – x = 80
⇒ 4x = 80
The sum of three consecutive odd numbers is 99. What is the difference of smallest and largest odd number?
Let the three consecutive odd numbers be x, x +2, x + 4.
∴ x + x + 2 + x + 4 = 99
⇒ 3x + 6 = 99
⇒ 3x = 93
⇒ x = 31
∴ The numbers are 31,33,35
Hence, difference = 35 – 31 = 4
The ages of Simran and Ranjna are in the ratio 5:3. After 6 years their ages will be in the ratio 7:5. What is present age of Ranjna?
Let Simran’s age = 5x
Ranjna’s age = 3x
After 6 years, Simran’s age = 5x + 6
Ranjna’s age = 3x + 6
⇒ 25x = 30 = 21x + 42
⇒ 25x –21x = 42 –30
⇒ 4x = 12
∴ Present age of Ranjana = 3x
= 3 × 3 = 9 years
Thrice a number when increased by 6 gives 84. What is that number?
Let the number be x.
∴ 3x + 6 = 84
⇒ 3x = 84 –6
⇒ 3x = 78
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