Which is the least number which when reduced by 5 is exactly divisible by 36,48,21 and 28?

Solution
Required number = LCM of (36,48,21 and 28) + 5
∴ LCM= 2 × 2 × 3 × 7 × 3 × 4 = 1008
∴ Required number = 1008 + 5= 1013
Find the nearest number to 99548 which is exactly divisible by 687:

Solution
687) 99548 (144
\(\frac{687}{3084}\)
\(\frac{2748}{3368}\)
\(\frac{2748}{620}\)
∴ Required number
= 99548 + (687  620)
= 99548 + 67 = 99615
Ram bought 12 tables for Rs. 12,000 and sold them at a profit equal to the cost price of 4 tables. Then, the selling price of 1 table is:

Solution
CP of 12 tables = Rs. 12000
= 12000 + 4x12000
∴ CP of 1 table
=\(\frac{1200}{12}\)=Rs.l000
According to the question,
SP of 12 tables = Rs. 16000
∴ SP of 1 table = \(\frac{1600}{12}\)
= Rs. 1333.33
What is the value of X if 4X = 5Y?

Solution
4X = 5Y
⇒Y=^{4}⁄_{5}x
From the figure
x + Y = 180°
⇒x+^{4}⁄_{5}y= 180°
\(\Rightarrow \frac{5X x 4X}{5}=180^{\circ}\)
⇒^{9x}⁄_{5}= 180°
⇒x=\(\frac{180^{\circ}\times 5}{9}=100^{\circ}\)
Under a scheme of investment,the rate of interest is 4% and the interest is compounded three monthly.What will be the amount if a man invests Rs.2,000 for 1 year under this scheme?

Solution
The interest is compounded quarterly.
∴ r=^{4}⁄_{4}=1%
Time 'T' = 4 quarter years
∴ Amount = P \(\left ( 1+\frac{R}{100} \right )^{T}\)
= 2000 \(\left ( 1+\frac{1}{100} \right )^{4}\)
= 2000 ×(1.01)^{4} = Rs. 2081.21
The rectangle measures 140m × 70m. The circle at its centre has a diameter of 28m. The area of the shaded portion
is :

Solution
Area of the shaded portion
= (140 × 70  π×(14)^{2})m^{2}
\(1=\left ( 9800\frac{22}{7}\times 14\times 14 \right )m^{2}\)
= (9800  616) m^{2} = 9184 m^{2}
In the given diagram below,AB = CD = 9m, AC = BD = 5m. Length and breadth of the unshaded portion are 3 m and 1m.
The area of the shaded portion is :

Solution
Area of the shaded portion
= (9 × 5  3 × 1) sq. m.
=42 Sq. m.
Afort has provision for 50 days. After 15 days a reinforcement of 150 men arrives and the provision now lasts 25 days. How many men were there in the fort?

Solution
Let there be x men in the garrison.
After 15 days, there was provision of food for x men for 35 days and for (x + 150) men the food lasted
for 25 days.
∴ More men, less days (Indirect)
x : x + 150 : : 25 : 35
⇒x x 35 = 25 (x + 150)
⇒x x 7 = 5 (x + 150)
⇒7x= 5x+ 750
⇒2x = 750
⇒X=^{750}⁄_{2}= 375
The White Mughals’ is authored by:

Solution
Mark Tully
The ICC woman cricket player of the year 2006 was :

Solution
Jhulan Goswami