The difference between the compound interest and the simple interest earned at the end of $3^{rd}$ year on a sum of money at a rate of $10\%$ per annum is Rs. $77.5.$ What is the sum? Rs. $3,500$ Rs. $2,500$ Rs. $3,000$ Rs. $2,000$

Aamir and Birju can cut $5000\;\text{g}$ of wood in $20$ min. Birju and Charles can cut $5000\;\text{g}$ of wood in $40$ min. Charles and Aamir cut $5\;\text{kg}$ of wood in $30$ min. How much time Charles will take to cut $5\;\text{kg}$ wood alone? $120$ min $48$ min $240$ min $120/7$ min

An alloy contains copper and zinc in the ratio $5:3$ and another contains copper and tin in the ratio $8:5.$ If equal weights of the two are melted together to form a $3^{rd}$ alloy, find the weight of tin per kg in the new alloy. $40/129$ $5/13$ $5/26$ $28/5$

$x$ is a whole number. If the only common factors of $x$ and $x2$ are $1$ and $x,$ then $x$ is ________. $1$ a perfect square an odd number a prime number

Line $AB$ is $24$ metres in length and is tangent to the inner one of the two concentric circles at point $C.$ Points $A$ and $B$ lie on the circumference of the outer circle. It is known that the radii of the two circles are integers. The radius of the outer circle is $13$ m $5$ m $7$ m $4$ m