In the annual examination Mahuya got 10%less marks than Supriyo in Mathematics. Mahuya got 81 marks. The marks of Supriyo are

Solution
Let the marks obtained by Supriyo be x.
Now, according to the question,
\(frac{9x}{10} = 81 Rightarrow x = frac{81 times 10}{9} = 90\)
In 1937, the Congress formed ministries in
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A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. The number of days in which B alone can finish the work is

Solution
Work done by A and B in 20 days = ^{20}⁄_{30} = ^{2}⁄_{3}
Remaining work = 1  ^{2}⁄_{3} = ^{1}⁄_{3}
Time taken by A in doing ^{1}⁄_{3} work = 20 days.
∴ A alone will complete the whole work in 60 days.
∴ B's 1 day's work = ^{1}⁄_{30}  ^{1}⁄_{60} = ^{1}⁄_{60}
∴ B alone will complete the work in 60 days.
Two trains, of same length, are running in parallel tracks in the same direction with speed 60 km/hour and 90 km/hour respectively. The latter completely crosses the former in 30 seconds. The length of each train (in metres) is

Solution
When two trains cross each other, they cover distance equal to the sum of their lengths with relative speed.
Let the length of each train be x metres.
∴ Relative speed = (90  60) = 30 kmph
= \(left ( frac{30 times 5}{18} right )\) m/sec = \(left ( frac{25}{3} right )\) m/sec
Now, according to the question
\(frac{2x}{frac{25}{3}} = 30\)
⇒ 2x = \(frac{30 times 25}{3}\) ⇔ 2x = 250 ⇔ x = 125 metres
If 6x – 5y = 13, 7x + 2y = 23, then 11x + 18y = ?

Solution
6x  5y = 13 (i)
7x + 2y = 23 (ii)
By equation (i) × 2 + (ii) × 5, we have,
\(frac{begin{matrix} 12x &  & 10y & = & 26\ 35x & + & 10y & = & 115 end{matrix}}{begin{matrix} 47x & ;;;; & ;;;; & = & 141 end{matrix}}\)
⇒ x = 3
From equation (i), we have,
6 × 3  5y = 13
⇒ 18  5y = 13 ⇔ 5y = 5 ⇔ y = 1
∴ 11x + 18y = 11 × 3 + 18 × 1 = 33 + 18 = 51
If \(\frac{xy}{x + y} = a, \frac{xz}{x + z} = b\) and \(\frac{yz}{y + z} = c\) where a, b, c are all nonzero numbers, then x equals to

Solution
\(frac{xy}{x + y} = a Rightarrow frac{x + y}{xy} = frac{1}{a}\)
⇒ \(frac{1}{y} + frac{1}{x} = frac{1}{a} ........left ( i right )\)
\(frac{xz}{x + z} = b Rightarrow frac{x + z}{xz} = frac{1}{b}\)
⇒ \(frac{1}{z} + frac{1}{x} = frac{1}{b} ........left ( ii right )\)
Similarly,
\(frac{1}{z} + frac{1}{y} = frac{1}{c} Rightarrow frac{1}{y} = frac{1}{c}  frac{1}{z} ........left ( iii right )\)
From equations (i) and (iii), we have,
\(frac{1}{a}  frac{1}{x} = frac{1}{c}  frac{1}{z} Rightarrow frac{1}{a}  frac{1}{x} = frac{1}{c}  frac{1}{b} + frac{1}{x}\)
[From equation(ii)]
⇒ \(frac{1}{x} + frac{1}{x} = frac{1}{a}  frac{1}{c} + frac{1}{b}\)
⇒ \(frac{2}{x} = frac{bc  ab + ac}{abc} Leftrightarrow x = frac{2abc}{ac + bc  ab}\)
Mohan sold his watch at 10% loss. lf he had sold it for Rs 45 more, he would have made 5% profit. The selling price (in Rs) of the watch was

Solution
Let the CP of watch be Rs x.
∴ First SP = Rs ^{9x}⁄_{10}
Now, according to the question
\(frac{105x}{100}  frac{9x}{10} = 45\)
⇒ \(frac{105x  90x}{100} = 45 Leftrightarrow frac{15x}{100} = 45\)
⇒ x = \(frac{45 times 100}{15} = Rs 300\)
∴ SP = Rs\(frac{300 times 9}{10}\) = Rs 270
Rama left home and walked 5 km southwards, turned right and walked 2 km and turned right and walked 5 km and turned left and walked 5 km. How many kilometres will she have to walk to reach her home straight?

Solution
Required distance = (5 + 2) = 7 km
Jaya started from house with son Rakesh and moved to North. Before signal point, Rakesh’s school bus took him to the right side. Jaya continued in the same line and got petrol filled in the scooter. Then she turned to her left and entered a supermarket. In which direction is the supermarket located from the petrol pump?

Solution
Supermarket is in the west from the petrol pump.
Four children, Akram, Bopsi, Priya and Tulsi are on a ladder. Akram is further up the ladder than Bopsi. Bopsi is in between Akram and Priya. If Tulsi is still further than Akram, who is the second person from the bottom?

Solution
Tulsi
Akram
Bopsi
Priya
If 16 ÷ 4 = 74
21 ÷ 7 = 33
81 ÷ 9 = 99
then 55 ÷ 5 =?

Solution