If P is the husband of Q and R is the mother of S and Q, what is R to P?

Solution
P is the husband of Q.
R is the mother of Q.
Therefore, R is motherinlaw of P.
By drawing family tree
Clearly, R is motherinlaw of P
In a group of equal number of cows and herdsmen the number of legs was 28 less than four times the number of heads. The number of herdsmen was

Solution
Suppose the number of cows = x
Therefore, the number of herdsmen = x
According to the question,
4 × 2x  28 = x × 2 + x × 4
⇒ 8x  28 = 2x + 4x ⇔ 8x  6x = 28
∴ x = ^{28}⁄_{2} = 14
In a family Mr Prakash has his wife and his two married brothers of whom one has two children and another has no issue. How many members are there in the family?

Solution
Mr Prakash and his wife = 2
Prakash's two married brothers = 4
Two children = 2
Total members = 8
Which one set of letters when sequentially placed at the gaps in the given letter series shall complete it ?
_ b _baaabb _ a _ _ bb _ a _

Solution
a b b b a a / a b b b a a / a b b b a a
Directions : In the following question which of the given responses would be a meaningful order of the following?
1. Birth
2. Death
3. Childhood
4. Infancy
5. Adolescence
6. Adulthood
7. Old age
The number of prime factors in 6^{333} × 7^{222} × 8^{111} is

Solution
6^{333} × 7^{222} × 8^{111}
∴ (2 × 3)^{333} × 7^{222} × (2^{3})^{111}
∴ 2^{333} × 3^{333} × 7^{222} × 2^{333}
∴ 2^{666} × 3^{333} × 7^{222}
∴ Number of prime factors = 666 + 333 + 222 = 1221
Let \(\sqrt[3]{a} = \sqrt[3]{26} + \sqrt[3]{7} + \sqrt[3]{63}\).
Then

Solution
\(sqrt[3]{a} = sqrt[3]{26} + sqrt[3]{7} + sqrt[3]{63}\)
⇒\(sqrt[3]{a} < sqrt[3]{27} + sqrt[3]{8} + sqrt[3]{64}\)
⇒ \(sqrt[3]{a} < 3 + 2 + 4 Leftrightarrow sqrt[3]{a} < 9\)
⇒ a < 9^{3} = 729
⇒ \(\frac{1}{7} + \left ( 999\frac{692}{693} \right ) \times 99\) is equal to

Solution
The given expression
\(frac{1}{7} + 999 times 99 + frac{692}{693} times 99\)
= \(frac{1}{7} + left( 1000  1 right) times 99 + frac{692}{7}\)
= \(frac{1}{7} + frac{692}{7} + 99000  99\)
= ^{693}⁄_{7} + 99000  99 = 99 + 99000  99 = 99000
In a division sum, the divisor is 3 times the quotient and 6 times the remainder. If the remainder is 2, then the dividend is

Solution
Divisor = 6 × 2 = 12
Again, Divisor = 3 × Quotient
∴ Quotient = ^{12}⁄_{3} = 4
Dividend = 12 × 4 + 2 = 48 + 2 = 50
If 120 is 20% of a number, then 120% of that number will be

Solution
let the number be x.
Now, according to the Question,
\(frac{x times 20}{100} = 120\)
⇒ x = 120 × 5 = 600
∴ 120% of 600 = \(frac{600 times 120}{100} = 720\)
A trader purchases a watch and a wall clock for 390. He sells them making a profit of 10% on the watch and 15% on the wall clock. He earns a profit of “51.50. The difference between the original prices of the wall clock and the watch is equal to

Solution
Let the CP of wrist watch be Rs x,then CP of wall clock would be Rs (390  x)
Now, according to the question,\(\frac{x\times 10}{100}+\frac{(390x)\times 15}{100}= 51.50\)
⇒ 1Ox+ 5850  15x = 5150
⇒ 5x= 5850  5150 = 700
\(⇒x=Rs\frac{700}{5} =Rs. 140\)
∴ CP of wall clock = 390  140 = Rs 250
∴ Required difference = Rs (250140) = Rs 110
A cricketer has a mean score of 60 runs in 10 innings. Find out how many runs are to be scored in the eleventh innings to raise the mean score to 62?

Solution
Required runs = 60 + 11 × 2 = 82 runs
In the afternoon, a student read 100 pages at the rate of 60 pages per hour. In the evening, when she was tired, she read 100 more pages at the rate of 40 pages per hour. What was her average rate of reading, in pages per hour?

Solution
Required average rate of reading
\(=\frac{100 + 100}{\frac{100}{60}+\frac{100}{40}}=\frac{200}{\frac{5}{3}+\frac{5}{2}}=\frac{200}{\frac{10+15}{6}}=\frac{200\times 6}{25}\)
In two types of stainless steel, the ratio of chromium and steel are 2 : 11 and 5 : 2 respectively. In what proportion should the two types be mixed so that the ratio of chromium to steel in the mixed type becomes 7 : 32 ?

Solution
Let the proportion be x : y.
In first type of stainless steel, the quantity of chromium = \(\frac{2x}{3}\) and the quantity of steel=\(\frac{11x}{13}\)In second type of stainless steel, the quantity of chromium = \(\frac{5y}{26}\) and the quantity of steel = \(\frac{21y}{26}\)
Now, according to the question
\(\frac{2x}{13}+\frac{5y}{26}:\frac{11x}{13}+\frac{21y}{26}=7:32\)
\(⇒\left ( \frac{2x}{13}+\frac{5y}{26} \right )\times 32=\left ( \frac{11x}{13}+\frac{21y}{26} \right )\times 7\)
\(⇒\left ( \frac{4x+5Y}{26} \right )\times 32=\left ( \frac{2X+21Y)}{26} \right )\times 7\)
⇒ 128X+ 160y= 154X+ 147y
⇒ 160y147y= 154X128X
⇒ 13y= 26X
\(⇒\frac{X}{Y}=\frac{13}{26}=\frac{1}{2}\)
∴ required ratio = 1 : 2
Method of Alligation:
Stainless Steel I II III
Chromium ^{2}⁄_{13} ^{5}⁄_{26} ^{7}⁄_{39}
\(=\frac{1514}{78}=\frac{1}{78}=\frac{76}{39}=\frac{1}{39}\)
∴ Required ratio =\(\frac{1}{78}:\frac{1}{39}\)=1:2
Direction: Select the related word or figure from the given options.
Direction : Select the related word or figure from the given options.
Crop: Farm: : Ore : ?

Solution
Crop is grown in the farm. Similarly, Ore is extracted from mine.
Directions : In each of the following questions, select the one which is different from the other three responses.

Solution
Except grass, all others can be obtained from animals and birds. Grass is a vegetation.
Directions : In each of the following questions, select the one which is different from the other three responses.

Solution
Except in number pair 525, in all others both the numbers are even numbers and the second number is perfect square of the first number. In the number pair 525 also the second number is the perfect square of the first number but both are odd numbers.
Directions : In each of the following questions, select the one which is different from the other three responses.

Solution
In figure (D), both the arrows are of equal length. In all other figures no two arrows are of equal lengths