Three friends divided some apples in the ratio $3 : 5 : 7$. After consuming 16 apples they found that the remaining number of apples with them was equal to the largest number of apples received by one of them at the beginning. The total number of apples these friends initially had was

The cost of a piece of jewellery is proportional to the square of its weight. A piece of jewellery weighing 10 grams is INR 3600. The cost of a piece of jewellery of the same kind weighing 4 grams is

In a company, initially the ratio of the foreign and domestic workers was 5 : 8. When some foreign and 12 domestic workers left the company, this ratio became 2 : 3. Later, when 10 more foreign workers were replaced by 10 new domestic workers, this ratio became 3 : 7. The initial number of domestic workers in the company was ___

Let $a, b, c, d$ be positive integers such that $a + b + c + d = 2023$. If $a: b = 2:5$ and $c:d=5:2$, then the maximum possible value of $a + c$ is

A fruit seller has oranges, apples, and bananas in the ratio $3:6:7$. If the number of oranges is a multiple of both 5 and 6, then the minimum number of fruits the seller has is:

Ashok purchased pens and pencils in the ratio $2:3$ during his first visit and paid Rs. 86 to the shopkeeper. During his second visit, he purchased pens and pencils in the ratio $4:1$ and paid Rs. 112. The cost of a pen as well as a pencil in rupees is a positive integer. If Ashok purchased four pens during his second visit, then the amount he paid in rupees for the pens during the second visit is __________.

$\dfrac{(a + b)}{(b + c)} = \dfrac{(c + d)}{(d + a)}$ which of the following statements is always true?