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Ram is three times as old as Mohan. Lokesh was twice as old as Ram four years ago. In four year’s time Ram will be 31. What is the difference between present ages of Mohan and Lokesh?
Let Ram’s age = x, Mohan’s age = y, Lokesh’s age = z
∴ x = 3y …(1)
and z – 4 = 2 (x – 4)
z = 2x – 8 + 4 = 2x – 4 …(2)
x + 4 = 31 ⇒ x = 27
3y = 27 ⇒ y = 9
Using eq. (2) z = 2x – 4 = 2 × 27 – 4 = 50
Hence z – y = 50 – 9 = 41
Rajesh got twice as many sums wrong as he got right. If he attempted 84 sums in all. How many sums did he solve correctly?
Let Rajesh solves x sums correctly
Right sums = x, wrong sums = 2x
∴ x + 2x = 84
⇒ 3x = 84
⇒ x = 28
Punam says, “If you reverse my own age, the figure represent my husband’s age. He is of course senior to me and the difference between our ages is one  eleventh of their sum. What is the age of Punam?
Let Punam’s age be 10x + y
∴ Her husband’s age = 10y + x
Now
10y + x – 10x – y = 1/11 (10y + x + 10x + y)
⇒
⇒
⇒ 9y – 9x = x + y
⇒ 9y – y = x + 9x
⇒ 8y = 10x
⇒
If y = 5, then x = 4
Hence, Punam’s age = 10 × 4 + 5 = 45 years.
A total of 324 coins of 20 paise & 25 paise make a sum of Rs. 71. What is the number of 25 paise coin?
Let the number of 25 paise coins be x
No. of 20 paise coins = 324 – x
∴ 0.20 (324 – x) + 0.25 × x = 71
⇒ 64.8 – 0.20x + 0.25x = 71
⇒ 0.05x = 71 – 64.8
⇒
In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of son is half that of his mother. The wife is 9 years younger than her husband and the brother is seven years older than his sister. What is the age of the mother?
Let the daughter’s age be x
Father’s age = 3x
Mother’s age = 3x – 9
Son’s age = x + 7
∴
⇒ 2x + 14 = 3x – 9 ⇒ x = 23
Mother’s age = 3x – 9 = 3 × 23 – 9 = 60 years
In a group of cows and hens, the number of legs are 14 more than twice the number of heads. What is the number of cows?
Let the number of cows be x & no. of hens be y
As per the question,
4x + 2y = 2 (x + y) + 14
⇒ 4x + 2y = 2x + 2y + 14
⇒ 2x = 14 ⇒ x = 7
If few sweets, have to be distributed. If I keep 2, 3, or 4 in a pack, I am left with one sweet. If I keep 5 in a pack I am left with none. What is the minimum number of sweets I have to pack and distribute?
If I keep 2 or 3 or 4 in a pack,
LCM of 2, 3, and 4 = 12
Then, the minimum number of sweets could be 12 + 1 = 13 so that 1 sweet left after packing.
But, if I keep 5 in a pack, I am left with none, (13 is not divisible by 5) then we have to take,
12 × 2 = 24
We have to add one so that 1 sweet left after packing in 2 or 3 or 4 groups and when in group of 5 then no sweets left. Therefore,
Total minimum sweets = 24 + 1 = 25 (25 is divisible by 5).
Hence, 25 is the correct answer.
In a city 40% of adults are illiterate while 85% of the children are literate. If the ratio of the adults to that of the children is 2 : 3, what percent of the population is litereted.
Let the no. of adults = 2x
No. of children = 3x
Literate population
= (100 – 40)% of 2x + 85% of 3x
= 60% of 2x + 85% of 3x
Literate percent =
A says, “If B gives me Rs. 40, he well have half as much as C, but if C gives me Rs. 40, then three of us will all have the same amount. What is the total amount of money that A, B & C have between them?
Given B – 40 = ⇒ 2B – 80 = C …(1)
and C – 40 = B …(2)
and C – 40 = A + 40 …(3)
From (1) & (2)
C = B + 40 = 120 + 40 = 160
160 – 40 = A + 40 ⇒ A = 160 – 80 = 80
7 + B + C = 80 + 120 + 160 = 360
Three bells ring after a regular interval of 36 seconds, 40 seconds and 48 seconds respectively. If the three bells start ringing at same time, then after how much time they will ring together?
To find the time in which all the bells ring together, we need to find the LCM of 36, 40, 48
Prime factorization of 36 = 2 × 2 × 3 × 3
Prime factorization of 40 = 2 × 2 × 2 × 5
Prime factorization of 48 = 2 × 2 × 2 × 2 × 3
Hence, LCM of 36, 40, 48 = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720 seconds.
∴
If a number is increased by 10% and then it is decreased by 10% then the value of number will
Let the number be 100
100 + 10% of 100 = 100 + 10 = 110
and 110 – 10% of 110 = 100 –
= 110 – 11 = 99
The cost price of 11 objects is Rs. 10 and the selling price of 10 objects is Rs. 11. What is the gain or loss percentage in whole transaction?
Cost price of 11 objects = Rs. 10
Cost price of 1 object = Rs.
Selling price of 10 objects = Rs. 11
Selling price of 1 object = Rs.
∴ Gain percent =
The total monthly income of 16 persons is Rs. 80800 and monthly income of one of the persons is greater than their average monthly income by 120%. What is the income of that person?
Average monthly income
Income of that person = 120% of 5050
= 12 × 505 = Rs. 6060
On a certain festival, sweets were to be equally distributed among 200 students. But 50 students were absent, therefore each student get 4 sweets extra. What is the number of sweets available for distribution?
Total no. of students = 200
Let the no. of sweets = x
∴
⇒
⇒ 200x – 150x = 4 × 150 × 200
⇒
Three friends had lunch at a restaurant. Arjun paid 2/3 as much as Jay paid and Jay paid 1/2 as much as Rakesh paid. What fraction of the bill did Jay pay?
Let Rakesh paid Rs. x.
Jay paid = x/2
Arjun paid =
∴ Total bill =
Part of Jay =
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