If sum of two numbers be a and their product be b, then the sum of their reciprocals is
If the number be x and y, then
x + y = a and xy = b
In a camp of 160 students provisions are available for 10 days. If 40 more students join the camp, how long will be provision last?
By, M1D1 = M2D2
⇒160 x 10 = 200 x D2
Discount on a pair of shoes marked at Rs. 475 and discounted at 15%, is
Required discount =
There taps A, B, C can fill an overhead tank in 4, 6 and 12 hours respectively. How long would be three taps take to fill the tank if all of them are opened together?
Part of the tank filled by all three taps in an hour
∴ Hence, the tank will be filled in 2 hours.
The cost price of an article is Rs. 100. A discount series of 5%, 10% successively reduces the price of a article by
Single equivalent discount
A grinder was marked at Rs. 3,600. After given a discount of 10% the dealer made a profit of 8%. Calculate the cost price.
Let the C.P. of grinder be = Rs x
If x2 + 9y2 = 6xy, then x : y is
x2 + 9y2 = 6xy
⇒ x2 – 6xy + 9y2 = 0
⇒ x2 – 2x.3y + (3y)2 = 0
⇒ (x – 3y)2 = 0
⇒ x – 3y = 0
⇒ x = 3y
⇒ x : y = 3 : 1
The average of 8 numbers is 27. If each of the numbers is multiplied by 8, find the average of new set of numbers.
If each item is multiplied by 8, their average gets multiplied by 8.
∴ Required average = 8 x 27 = 216
If the profit on sale price be 20%, the percentage of profit on cost price is
If S.P. = Rs 100, then gain = Rs 20
∴ C.P. = 100 – 20 = Rs 80
A container containing 400 litres of oil lost 8% by leakage. Oil left on the container is
Remaining oil in container
In an election, three candidates contested. The first candidate got 40% votes and the second got 36% votes. If total number of votes polled were 36000, find the number of votes got by the 3rd candidate.
Vote percentage of third candidate
= 100 – 40 – 36 = 24%
∴ Votes got by third candidate
A train, 120 m long, takes 6 seconds to pass a telegraph post; the speed of train is
Speed of train
Atrain travelled at a speed of 35 km/hr for the first 10 minutes and at a speed of 20 km/hr for the next 5 minutes. The average speed of the train for the total 15 minutes is
Total time = 15 minutes
If x : y :: 2 : 3 and 2 : x : 4 : 8 the value of y is
Here x : y :: 2 : 3
2 : x :: 4 : 8
If 40% of of a number is 48, then what is 1% of the same number?
Here 40% of of number = 48
Let number = x
A train 50 metre long passes a platform 100 metre long in 10 sec. The speed of the train in km/hr is
Speed of train
Rs. 730 were divided among A, B, C in such a way that if A gets Rs. 3, then B gets Rs. 4 and if B gets Rs. 3.50 then C gets Rs. 3. The share of B exceeds that of C by
Given A : B = 3 : 4
B : C = 3.50 : 3
(Here A = Rs 3, B = Rs4)
Now share of B exceeds that of C by
Mahesh earned a profit of 20% by selling 60 apples at the rate of Rs. 51 for 6 apples. Then the total cost, at which the apples were bought is
In a prep school, the average weight of 30 girls in a class among 50 students is 16 kg and that of the remaining students is 15.5 kg. What is the average weight of all the students in the class?
A boy found that the average of 20 numbers is 35 when he writes a number ‘61’ instead of ‘16’. The correct average of 20 numbers is
Average of 20 numbers = 20 x 35 = 700
Here difference of a number = 61 – 16 = 45
Now correct average of 20 number = 35 – 2.25 = 32.75