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The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?
Let the smaller number be x.
Then larger number = (x + 1365).
∴ x + 1365 = 6x + 15
⇒ 5x = 1350
⇒ x = 270
Smaller number = 270.
On dividing a number by 5, we get 3 as the remainder. What will the remainder be when the square of this number is divided by 5?
Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
∴ x = 5k + 3
∴ x^{2} = (5k +3)^{2}
= (25k^{2} + 30k + 9)
= 5(5k^{2} + 6k+1) + 4
∴ on dividing x^{2} by 5, we get 4 as remainder.
From his house, Lokesh went 15 kms to the North. Then he turned West and covered 10 kms. Then he turned South and covered 5 kms. Finally, turning to East, he covered 10 kms. In which direction is he from his house?
Final position of Lokesh is at point ‘E’ which is north from his house.
Directions: Given here is a multiple bar diagram of the scores of four players in two innings. Study the diagram and answer the questions.
The who scored highest average runs of two innings is:
Required average runs scored by MS Dhoni
Required average runs scored by S Raina
Required average runs scored by R Sharma
Required average runs scored by H Pandya
The required cricketer is M.S. Dhoni.
Directions: Given here is a multiple bar diagram of the scores of four players in two innings. Study the diagram and answer the questions.
The total scores in the first innings contributed by the four players is
Required total score = 60 + 50 + 55 + 50 = 215
Group the following figures into three classes using each figure only once
1, 5, 7 contain a rectangle with its two diagonals as the outer element and another element (similar or different) placed inside it.
2, 6, 9 contain a triangle with its three medians as the outer element and another element (similar or different) placed inside it.
3, 4, 8 contain a circle with its two mutually perpendicular diameters as the outer element and another element (similar or different) placed inside it.
The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is
L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3 ) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683.
In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quantity of water to be further added is
Quantity of M ilk = 60 x (2/3) = 40 liters Quantity of water = 60  40 = 20 liters
As per question we need to add water to get quantity 1:2
⇒ 40/(20 + x) = 1/2
⇒ 20 + x = 80
⇒ x = 60 liters
A rectangular lawn is 120 m by 90 m and has two roads each 15m wide running in the middle of it. One parallel to its length and other parallel to the breadth. Find the cost of gravelling the road at ₹ 20 per sq meter.
According to question,
Area of road that is parallel to length
= 120 x 15 = 1800 sq m
Area of road that is parallel to breadth
= 90 x 15 = 1350 sqm
Area of intersection of two roads
= 15 x 15 = 22m^{2}
∴ Area of two road = (1800+ 1350225)
= 2925 sq m
Cost at 1 sq m = 20
So, Cost at 2925 sq m = 20 x 2925
= ₹ 58500
There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is
According to question
so d = 13
A courtyard is 25 meters long and 16 meters board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is :
A rectangular grassy plot is 112 m by 78 m. It has a gravel path 2.5 m wide all round it on the inside. Find the cost of constructing it at ₹ 2 per square meter?
Are of path = 2 x (1 + b  2x)
= 5 (112 + 78  5)
= 5 * 185 = 925 sq m
Therefore, Required cost = (925x2)
= ₹ 1850
Find the area of the shaded region in the figure:
Step 1: Findarea of inner square
= 2 cm x 2 cm = 4 cm^{2}
Step 2 : Find area of outer shape
= (2 cm x 3 cm) + (10 cm x 3 cm)
= 6 cm^{2} + 30 cm^{2} = 36 cm^{2}
Step 3 : Area of shaded region
= area of outer shape  area of inner square
= 36 cm^{2}  4 cm^{2} = 32 cm^{2}
A man buys an item at ₹ 1200 and sells it at the loss of 20 percent. Then what is the selling price of that item?
Here always remember, when ever, x% loss,
it means S.P. = (100  x) % of C.P
When ever, x% profit, it means S.P. = (100 + x) % of C.P
So here will be (100  x) % of C.P.
= 80 % of 1200
= 80/100 x 1200
= 960
Ram walks 2 km to the East, and then he turns to South and walks 6 km. He again turns to East and walks 2 km. Then he turns to North and walks 12 km. How far is he from the starting point?
Required distance
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